---
OA_place: publisher
_id: '20563'
abstract:
- lang: eng
text: "The theory of optimal transport provides an elegant and powerful description
of many evolution\r\nequations as gradient flows. The primary objective of this
thesis is to adapt and extend the\r\ntheory to deal with important equations that
are not covered by the classical framework,\r\nspecifically boundary value problems
and kinetic equations. Additionally, we establish new\r\nresults in periodic homogenization
for discrete dynamical optimal transport and in quantization\r\nof measures.\r\nSection
1.1 serves as an invitation to the classical theory of optimal transport, including
the\r\nmain definitions and a selection of well-established theorems. Sections
1.2-1.5 introduce the\r\nmain results of this thesis, outline the motivations,
and review the current state of the art.\r\nIn Chapter 2, we consider the Fokker–Planck
equation on a bounded set with positive Dirichlet\r\nboundary conditions. We construct
a time-discrete scheme involving a modification of the\r\nWasserstein distance
and, under weak assumptions, prove its convergence to a solution of this\r\nboundary
value problem. In dimension 1, we show that this solution is a gradient flow in
a\r\nsuitable space of measures.\r\nChapter 3 presents joint work with Giovanni
Brigati and Jan Maas. We introduce a new theory\r\nof optimal transport to describe
and study particle systems at the mesoscopic scale. We prove\r\nadapted versions
of some fundamental theorems, including the Benamou–Brenier formula and\r\nthe
identification of absolutely continuous curves of measures.\r\nChapter 4 presents
joint work with Lorenzo Portinale. We prove convergence of dynamical\r\ntransportation
functionals on periodic graphs in the large-scale limit when the cost functional\r\nis
asymptotically linear. Additionally, we show that discrete 1-Wasserstein distances
converge\r\nto 1-Wasserstein distances constructed from crystalline norms on R\r\nd\r\n.\r\nChapter
5 concerns optimal empirical quantization: the problem of approximating a measure\r\nby
the sum of n equally weighted Dirac deltas, so as to minimize the error in the
p-Wasserstein\r\ndistance. Our main result is an analog of Zador’s theorem, providing
asymptotic bounds for\r\nthe minimal error as n tends to infinity.\r\n"
acknowledgement: "The research contained in this thesis has received funding from
the Austrian Science\r\nFund (FWF) project 10.55776/F65."
alternative_title:
- ISTA Thesis
article_processing_charge: No
author:
- first_name: Filippo
full_name: Quattrocchi, Filippo
id: 3ebd6ba8-edfb-11eb-afb5-91a9745ba308
last_name: Quattrocchi
orcid: 0009-0000-9773-1931
citation:
ama: Quattrocchi F. Optimal transport methods for kinetic equations, boundary value
problems, and discretization of measures. 2025. doi:10.15479/AT-ISTA-20563
apa: Quattrocchi, F. (2025). Optimal transport methods for kinetic equations,
boundary value problems, and discretization of measures. Institute of Science
and Technology Austria. https://doi.org/10.15479/AT-ISTA-20563
chicago: Quattrocchi, Filippo. “Optimal Transport Methods for Kinetic Equations,
Boundary Value Problems, and Discretization of Measures.” Institute of Science
and Technology Austria, 2025. https://doi.org/10.15479/AT-ISTA-20563.
ieee: F. Quattrocchi, “Optimal transport methods for kinetic equations, boundary
value problems, and discretization of measures,” Institute of Science and Technology
Austria, 2025.
ista: Quattrocchi F. 2025. Optimal transport methods for kinetic equations, boundary
value problems, and discretization of measures. Institute of Science and Technology
Austria.
mla: Quattrocchi, Filippo. Optimal Transport Methods for Kinetic Equations, Boundary
Value Problems, and Discretization of Measures. Institute of Science and Technology
Austria, 2025, doi:10.15479/AT-ISTA-20563.
short: F. Quattrocchi, Optimal Transport Methods for Kinetic Equations, Boundary
Value Problems, and Discretization of Measures, Institute of Science and Technology
Austria, 2025.
corr_author: '1'
date_created: 2025-10-28T13:10:49Z
date_published: 2025-11-03T00:00:00Z
date_updated: 2026-06-18T18:02:13Z
day: '03'
ddc:
- '515'
- '519'
degree_awarded: PhD
department:
- _id: GradSch
- _id: JaMa
doi: 10.15479/AT-ISTA-20563
file:
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checksum: 6f55275bdf99992be3a6457d949dd664
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creator: fquattro
date_created: 2025-11-17T21:04:15Z
date_updated: 2026-01-01T23:30:03Z
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date_updated: 2026-01-01T23:30:03Z
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file_name: 2025_quattrocchi_thesis.zip
file_size: 11726509
relation: source_file
file_date_updated: 2026-01-01T23:30:03Z
has_accepted_license: '1'
keyword:
- optimal transport
- kinetic equations
- boundary value problems
- quantization
- gradient flows
- homogenization
language:
- iso: eng
month: '11'
oa: 1
oa_version: Published Version
page: '240'
project:
- _id: 260482E2-B435-11E9-9278-68D0E5697425
call_identifier: FWF
grant_number: F06504
name: Taming Complexity in Partial Differential Systems
publication_identifier:
issn:
- 2663-337X
publication_status: published
publisher: Institute of Science and Technology Austria
related_material:
record:
- id: '20569'
relation: part_of_dissertation
status: public
- id: '20571'
relation: part_of_dissertation
status: public
- id: '20570'
relation: part_of_dissertation
status: public
- id: '18706'
relation: part_of_dissertation
status: public
status: public
supervisor:
- first_name: Jan
full_name: Maas, Jan
id: 4C5696CE-F248-11E8-B48F-1D18A9856A87
last_name: Maas
orcid: 0000-0002-0845-1338
title: Optimal transport methods for kinetic equations, boundary value problems, and
discretization of measures
tmp:
image: /images/cc_by.png
legal_code_url: https://creativecommons.org/licenses/by/4.0/legalcode
name: Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)
short: CC BY (4.0)
type: dissertation
user_id: ba8df636-2132-11f1-aed0-ed93e2281fdd
year: '2025'
...
---
OA_place: repository
OA_type: green
_id: '20569'
abstract:
- lang: eng
text: 'This is the first part of a general description in terms of mass transport
for time-evolving interacting particles systems, at a mesoscopic level. Beyond
kinetic theory, our framework naturally applies in biology, computer vision, and
engineering. The central object of our study is a new discrepancy d between two
probability distributions in position and velocity states, which is reminiscent
of the 2-Wasserstein distance, but of second-order nature. We construct d in two
steps. First, we optimise over transport plans. The cost function is given by
the minimal acceleration between two coupled states on a fixed time horizon T.
Second, we further optimise over the time horizon T > 0. We prove the existence
of optimal transport plans and maps, and study two time-continuous characterisations
of d. One is given in terms of dynamical transport plans. The other one -- in
the spirit of the Benamou--Brenier formula -- is formulated as the minimisation
of an action of the acceleration field, constrained by Vlasov''s equations. Equivalence
of static and dynamical formulations of d holds true. While part of this result
can be derived from recent, parallel developments in optimal control between measures,
we give an original proof relying on two new ingredients: Galilean regularisation
of Vlasov''s equations and a kinetic Monge--Mather shortening principle. Finally,
we establish a first-order differential calculus in the geometry induced by d,
and identify solutions to Vlasov''s equations with curves of measures satisfying
a certain d-absolute continuity condition. One consequence is an explicit formula
for the d-derivative of such curves.'
acknowledgement: "This work was partially inspired by an unpublished note from 2014
by Guillaume Carlier,\r\nJean Dolbeault, and Bruno Nazaret. GB deeply thanks Jean
Dolbeault for proposing\r\nthis problem to him, guiding him into the subject, and
sharing the aforementioned note.\r\nWe are grateful to Karthik Elamvazhuthi for
making us aware of the work [20].\r\nThe work of GB has received funding from the
European Union’s Horizon 2020 research and innovation programme under the Marie
Sklodowska-Curie grant agreement\r\nNo 101034413.\r\nJM and FQ gratefully acknowledge
support from the Austrian Science Fund (FWF)\r\nproject 10.55776/F65."
article_number: '2502.15665'
article_processing_charge: No
arxiv: 1
author:
- first_name: Giovanni
full_name: Brigati, Giovanni
id: 63ff57e8-1fbb-11ee-88f2-f558ffc59cf1
last_name: Brigati
- first_name: Jan
full_name: Maas, Jan
id: 4C5696CE-F248-11E8-B48F-1D18A9856A87
last_name: Maas
orcid: 0000-0002-0845-1338
- first_name: Filippo
full_name: Quattrocchi, Filippo
id: 3ebd6ba8-edfb-11eb-afb5-91a9745ba308
last_name: Quattrocchi
orcid: 0009-0000-9773-1931
citation:
ama: 'Brigati G, Maas J, Quattrocchi F. Kinetic Optimal Transport (OTIKIN) -- Part
1: Second-order discrepancies between probability measures. arXiv. doi:10.48550/arXiv.2502.15665'
apa: 'Brigati, G., Maas, J., & Quattrocchi, F. (n.d.). Kinetic Optimal Transport
(OTIKIN) -- Part 1: Second-order discrepancies between probability measures. arXiv.
https://doi.org/10.48550/arXiv.2502.15665'
chicago: 'Brigati, Giovanni, Jan Maas, and Filippo Quattrocchi. “Kinetic Optimal
Transport (OTIKIN) -- Part 1: Second-Order Discrepancies between Probability Measures.”
ArXiv, n.d. https://doi.org/10.48550/arXiv.2502.15665.'
ieee: 'G. Brigati, J. Maas, and F. Quattrocchi, “Kinetic Optimal Transport (OTIKIN)
-- Part 1: Second-order discrepancies between probability measures,” arXiv.
.'
ista: 'Brigati G, Maas J, Quattrocchi F. Kinetic Optimal Transport (OTIKIN) -- Part
1: Second-order discrepancies between probability measures. arXiv, 2502.15665.'
mla: 'Brigati, Giovanni, et al. “Kinetic Optimal Transport (OTIKIN) -- Part 1: Second-Order
Discrepancies between Probability Measures.” ArXiv, 2502.15665, doi:10.48550/arXiv.2502.15665.'
short: G. Brigati, J. Maas, F. Quattrocchi, ArXiv (n.d.).
corr_author: '1'
date_created: 2025-10-28T13:12:08Z
date_published: 2025-08-10T00:00:00Z
date_updated: 2026-06-28T22:30:41Z
day: '10'
department:
- _id: GradSch
- _id: JaMa
doi: 10.48550/arXiv.2502.15665
ec_funded: 1
external_id:
arxiv:
- '2502.15665'
keyword:
- optimal transport
- kinetic theory
- second-order discrepancy
- Vlasov equation
- Wasserstein splines.
language:
- iso: eng
main_file_link:
- open_access: '1'
url: https://doi.org/10.48550/arXiv.2502.15665
month: '08'
oa: 1
oa_version: Preprint
project:
- _id: fc31cba2-9c52-11eb-aca3-ff467d239cd2
grant_number: F6504
name: Taming Complexity in Partial Differential Systems
- _id: fc2ed2f7-9c52-11eb-aca3-c01059dda49c
call_identifier: H2020
grant_number: '101034413'
name: 'IST-BRIDGE: International postdoctoral program'
publication: arXiv
publication_status: draft
related_material:
record:
- id: '20563'
relation: dissertation_contains
status: public
status: public
title: 'Kinetic Optimal Transport (OTIKIN) -- Part 1: Second-order discrepancies between
probability measures'
type: preprint
user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87
year: '2025'
...
---
OA_place: publisher
OA_type: hybrid
_id: '14703'
abstract:
- lang: eng
text: We present a discretization of the dynamic optimal transport problem for which
we can obtain the convergence rate for the value of the transport cost to its
continuous value when the temporal and spatial stepsize vanish. This convergence
result does not require any regularity assumption on the measures, though experiments
suggest that the rate is not sharp. Via an analysis of the duality gap we also
obtain the convergence rates for the gradient of the optimal potentials and the
velocity field under mild regularity assumptions. To obtain such rates we discretize
the dual formulation of the dynamic optimal transport problem and use the mature
literature related to the error due to discretizing the Hamilton-Jacobi equation.
acknowledgement: 'The authors would like to thank Chris Wojtan for his continuous
support and several interesting discussions. Part of this research was performed
during two visits: one of SI to the BIDSA research center at Bocconi University,
and one of HL to the Institute of Science and Technology Austria. Both host institutions
are warmly acknowledged for the hospitality. HL is partially supported by the MUR-Prin
2022-202244A7YL “Gradient Flows and Non-Smooth Geometric Structures with Applications
to Optimization and Machine Learning”, funded by the European Union - Next Generation
EU. SI is supported in part by ERC Consolidator Grant 101045083 “CoDiNA” funded
by the European Research Council.'
article_processing_charge: Yes (via OA deal)
article_type: original
arxiv: 1
author:
- first_name: Sadashige
full_name: Ishida, Sadashige
id: 6F7C4B96-A8E9-11E9-A7CA-09ECE5697425
last_name: Ishida
orcid: 0000-0002-3121-3100
- first_name: Hugo
full_name: Lavenant, Hugo
last_name: Lavenant
citation:
ama: Ishida S, Lavenant H. Quantitative convergence of a discretization of dynamic
optimal transport using the dual formulation. Foundations of Computational
Mathematics. 2024. doi:10.1007/s10208-024-09686-3
apa: Ishida, S., & Lavenant, H. (2024). Quantitative convergence of a discretization
of dynamic optimal transport using the dual formulation. Foundations of Computational
Mathematics. Springer Nature. https://doi.org/10.1007/s10208-024-09686-3
chicago: Ishida, Sadashige, and Hugo Lavenant. “Quantitative Convergence of a Discretization
of Dynamic Optimal Transport Using the Dual Formulation.” Foundations of Computational
Mathematics. Springer Nature, 2024. https://doi.org/10.1007/s10208-024-09686-3.
ieee: S. Ishida and H. Lavenant, “Quantitative convergence of a discretization of
dynamic optimal transport using the dual formulation,” Foundations of Computational
Mathematics. Springer Nature, 2024.
ista: Ishida S, Lavenant H. 2024. Quantitative convergence of a discretization of
dynamic optimal transport using the dual formulation. Foundations of Computational
Mathematics.
mla: Ishida, Sadashige, and Hugo Lavenant. “Quantitative Convergence of a Discretization
of Dynamic Optimal Transport Using the Dual Formulation.” Foundations of Computational
Mathematics, Springer Nature, 2024, doi:10.1007/s10208-024-09686-3.
short: S. Ishida, H. Lavenant, Foundations of Computational Mathematics (2024).
corr_author: '1'
date_created: 2023-12-21T10:14:37Z
date_published: 2024-11-11T00:00:00Z
date_updated: 2026-06-18T17:37:10Z
day: '11'
ddc:
- '000'
department:
- _id: GradSch
- _id: ChWo
doi: 10.1007/s10208-024-09686-3
external_id:
arxiv:
- '2312.12213'
isi:
- '001352503300001'
isi: 1
keyword:
- Optimal transport
- Hamilton-Jacobi equation
- convex optimization
language:
- iso: eng
main_file_link:
- open_access: '1'
url: https://doi.org/10.1007/s10208-024-09686-3
month: '11'
oa: 1
oa_version: Published Version
project:
- _id: 34bc2376-11ca-11ed-8bc3-9a3b3961a088
grant_number: '101045083'
name: Computational Discovery of Numerical Algorithms for Animation and Simulation
of Natural Phenomena
publication: Foundations of Computational Mathematics
publication_identifier:
eissn:
- 1615-3383
issn:
- 1615-3375
publication_status: epub_ahead
publisher: Springer Nature
quality_controlled: '1'
scopus_import: '1'
status: public
title: Quantitative convergence of a discretization of dynamic optimal transport using
the dual formulation
type: journal_article
user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87
year: '2024'
...
---
OA_place: repository
OA_type: green
_id: '20571'
abstract:
- lang: eng
text: "We prove the convergence of a modified Jordan--Kinderlehrer--Otto scheme
to a solution to the Fokker--Planck equation in $\\Omega \\Subset \\mathbb{R}^d$
with general, positive and temporally constant, Dirichlet boundary conditions.
We work under mild assumptions on the domain, the drift, and the initial datum.
\ In the special case where $\\Omega$ is an interval in $\\mathbb{R}^1$, we prove
that such a solution is a gradient flow -- curve of maximal slope -- within a
suitable space of measures, endowed with a modified Wasserstein distance.\r\nOur
discrete scheme and modified distance draw inspiration from contributions by A.
Figalli and N. Gigli [J. Math. Pures Appl. 94, (2010), pp. 107--130], and J. Morales
[J. Math. Pures Appl. 112, (2018), pp. 41--88] on an optimal-transport approach
to evolution equations with Dirichlet boundary conditions. Similarly to these
works, we allow the mass to flow from/to the boundary $\\partial \\Omega$ throughout
the evolution. However, our leading idea is to also keep track of the mass at
the boundary by working with measures defined on the whole closure $\\overline
\\Omega$. The driving functional is a modification of the classical relative entropy
that also makes use of the information at the boundary. As an intermediate result,
when $\\Omega$ is an interval in $\\mathbb{R}^1$, we find a formula for the descending
slope of this geodesically nonconvex functional. "
acknowledgement: "The author would like to thank Jan Maas for suggesting this project
and for many helpful\r\ncomments, Antonio Agresti, Lorenzo Dello Schiavo and Julian
Fischer for several fruitful discussions, and Oliver Tse for pointing out the reference
[15]. He also gratefully acknowledges support from the Austrian Science Fund (FWF)
project 10.55776/F65.\r\n"
article_number: '2403.07803'
article_processing_charge: No
arxiv: 1
author:
- first_name: Filippo
full_name: Quattrocchi, Filippo
id: 3ebd6ba8-edfb-11eb-afb5-91a9745ba308
last_name: Quattrocchi
orcid: 0009-0000-9773-1931
citation:
ama: Quattrocchi F. Variational structures for the Fokker-Planck equation with general
Dirichlet boundary conditions. arXiv. doi:10.48550/arXiv.2403.07803
apa: Quattrocchi, F. (n.d.). Variational structures for the Fokker-Planck equation
with general Dirichlet boundary conditions. arXiv. https://doi.org/10.48550/arXiv.2403.07803
chicago: Quattrocchi, Filippo. “Variational Structures for the Fokker-Planck Equation
with General Dirichlet Boundary Conditions.” ArXiv, n.d. https://doi.org/10.48550/arXiv.2403.07803.
ieee: F. Quattrocchi, “Variational structures for the Fokker-Planck equation with
general Dirichlet boundary conditions,” arXiv. .
ista: Quattrocchi F. Variational structures for the Fokker-Planck equation with
general Dirichlet boundary conditions. arXiv, 2403.07803.
mla: Quattrocchi, Filippo. “Variational Structures for the Fokker-Planck Equation
with General Dirichlet Boundary Conditions.” ArXiv, 2403.07803, doi:10.48550/arXiv.2403.07803.
short: F. Quattrocchi, ArXiv (n.d.).
corr_author: '1'
date_created: 2025-10-28T13:12:56Z
date_published: 2024-04-09T00:00:00Z
date_updated: 2026-06-28T22:30:41Z
day: '09'
department:
- _id: GradSch
- _id: JaMa
doi: 10.48550/arXiv.2403.07803
external_id:
arxiv:
- '2403.07803'
keyword:
- gradient flows
- Jordan–Kinderlehrer–Otto scheme
- curves of maximal slope
- optimal transport
- Dirichlet boundary conditions
- Fokker–Planck equation
language:
- iso: eng
main_file_link:
- open_access: '1'
url: https://doi.org/10.48550/arXiv.2403.07803
month: '04'
oa: 1
oa_version: Preprint
project:
- _id: 260482E2-B435-11E9-9278-68D0E5697425
call_identifier: FWF
grant_number: F06504
name: Taming Complexity in Partial Differential Systems
publication: arXiv
publication_status: draft
related_material:
record:
- id: '20865'
relation: later_version
status: public
- id: '20563'
relation: dissertation_contains
status: public
status: public
title: Variational structures for the Fokker-Planck equation with general Dirichlet
boundary conditions
type: preprint
user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87
year: '2024'
...
---
OA_place: repository
OA_type: green
_id: '20570'
abstract:
- lang: eng
text: "We investigate the minimal error in approximating a general probability\r\nmeasure
$\\mu$ on $\\mathbb{R}^d$ by the uniform measure on a finite set with\r\nprescribed
cardinality $n$. The error is measured in the $p$-Wasserstein\r\ndistance. In
particular, when $1\\le parXiv. doi:10.48550/arXiv.2408.12924
apa: Quattrocchi, F. (n.d.). Asymptotics for optimal empirical quantization of measures.
arXiv. https://doi.org/10.48550/arXiv.2408.12924
chicago: Quattrocchi, Filippo. “Asymptotics for Optimal Empirical Quantization of
Measures.” ArXiv, n.d. https://doi.org/10.48550/arXiv.2408.12924.
ieee: F. Quattrocchi, “Asymptotics for optimal empirical quantization of measures,”
arXiv. .
ista: Quattrocchi F. Asymptotics for optimal empirical quantization of measures.
arXiv, 2408.12924.
mla: Quattrocchi, Filippo. “Asymptotics for Optimal Empirical Quantization of Measures.”
ArXiv, 2408.12924, doi:10.48550/arXiv.2408.12924.
short: F. Quattrocchi, ArXiv (n.d.).
corr_author: '1'
date_created: 2025-10-28T13:12:22Z
date_published: 2024-08-23T00:00:00Z
date_updated: 2026-06-28T22:30:41Z
day: '23'
department:
- _id: GradSch
- _id: JaMa
doi: 10.48550/arXiv.2408.12924
external_id:
arxiv:
- '2408.12924'
keyword:
- optimal empirical quantization
- vector quantization
- Wasserstein distance
- semidiscrete optimal transport
- Zador’s Theorem
- Pierce’s Lemma
language:
- iso: eng
main_file_link:
- open_access: '1'
url: https://doi.org/10.48550/arXiv.2408.12924
month: '08'
oa: 1
oa_version: Preprint
project:
- _id: 260482E2-B435-11E9-9278-68D0E5697425
call_identifier: FWF
grant_number: F06504
name: Taming Complexity in Partial Differential Systems
publication: arXiv
publication_status: draft
related_material:
record:
- id: '20563'
relation: dissertation_contains
status: public
status: public
title: Asymptotics for optimal empirical quantization of measures
type: preprint
user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87
year: '2024'
...
---
_id: '10553'
abstract:
- lang: eng
text: The popularity of permissioned blockchain systems demands BFT SMR protocols
that are efficient under good network conditions (synchrony) and robust under
bad network conditions (asynchrony). The state-of-the-art partially synchronous
BFT SMR protocols provide optimal linear communication cost per decision under
synchrony and good leaders, but lose liveness under asynchrony. On the other hand,
the state-of-the-art asynchronous BFT SMR protocols are live even under asynchrony,
but always pay quadratic cost even under synchrony. In this paper, we propose
a BFT SMR protocol that achieves the best of both worlds -- optimal linear cost
per decision under good networks and leaders, optimal quadratic cost per decision
under bad networks, and remains always live.
article_processing_charge: No
arxiv: 1
author:
- first_name: Rati
full_name: Gelashvili, Rati
last_name: Gelashvili
- first_name: Eleftherios
full_name: Kokoris Kogias, Eleftherios
id: f5983044-d7ef-11ea-ac6d-fd1430a26d30
last_name: Kokoris Kogias
- first_name: Alexander
full_name: Spiegelman, Alexander
last_name: Spiegelman
- first_name: Zhuolun
full_name: Xiang, Zhuolun
last_name: Xiang
citation:
ama: 'Gelashvili R, Kokoris Kogias E, Spiegelman A, Xiang Z. Brief announcement:
Be prepared when network goes bad: An asynchronous view-change protocol. In: Proceedings
of the 2021 ACM Symposium on Principles of Distributed Computing. Association
for Computing Machinery; 2021:187-190. doi:10.1145/3465084.3467941'
apa: 'Gelashvili, R., Kokoris Kogias, E., Spiegelman, A., & Xiang, Z. (2021).
Brief announcement: Be prepared when network goes bad: An asynchronous view-change
protocol. In Proceedings of the 2021 ACM Symposium on Principles of Distributed
Computing (pp. 187–190). Virtual, Italy: Association for Computing Machinery.
https://doi.org/10.1145/3465084.3467941'
chicago: 'Gelashvili, Rati, Eleftherios Kokoris Kogias, Alexander Spiegelman, and
Zhuolun Xiang. “Brief Announcement: Be Prepared When Network Goes Bad: An Asynchronous
View-Change Protocol.” In Proceedings of the 2021 ACM Symposium on Principles
of Distributed Computing, 187–90. Association for Computing Machinery, 2021.
https://doi.org/10.1145/3465084.3467941.'
ieee: 'R. Gelashvili, E. Kokoris Kogias, A. Spiegelman, and Z. Xiang, “Brief announcement:
Be prepared when network goes bad: An asynchronous view-change protocol,” in Proceedings
of the 2021 ACM Symposium on Principles of Distributed Computing, Virtual,
Italy, 2021, pp. 187–190.'
ista: 'Gelashvili R, Kokoris Kogias E, Spiegelman A, Xiang Z. 2021. Brief announcement:
Be prepared when network goes bad: An asynchronous view-change protocol. Proceedings
of the 2021 ACM Symposium on Principles of Distributed Computing. PODC: Principles
of Distributed Computing, 187–190.'
mla: 'Gelashvili, Rati, et al. “Brief Announcement: Be Prepared When Network Goes
Bad: An Asynchronous View-Change Protocol.” Proceedings of the 2021 ACM Symposium
on Principles of Distributed Computing, Association for Computing Machinery,
2021, pp. 187–90, doi:10.1145/3465084.3467941.'
short: R. Gelashvili, E. Kokoris Kogias, A. Spiegelman, Z. Xiang, in:, Proceedings
of the 2021 ACM Symposium on Principles of Distributed Computing, Association
for Computing Machinery, 2021, pp. 187–190.
conference:
end_date: 2021-07-30
location: Virtual, Italy
name: 'PODC: Principles of Distributed Computing'
start_date: 2021-07-26
date_created: 2021-12-16T13:20:19Z
date_published: 2021-07-21T00:00:00Z
date_updated: 2023-09-04T11:42:10Z
day: '21'
department:
- _id: ElKo
doi: 10.1145/3465084.3467941
external_id:
arxiv:
- '2103.03181'
isi:
- '000744439800018'
isi: 1
keyword:
- optimal
- state machine replication
- fallback
- asynchrony
- byzantine faults
language:
- iso: eng
main_file_link:
- open_access: '1'
url: https://arxiv.org/abs/2103.03181
month: '07'
oa: 1
oa_version: Preprint
page: 187-190
publication: Proceedings of the 2021 ACM Symposium on Principles of Distributed Computing
publication_identifier:
isbn:
- 9-781-4503-8548-0
publication_status: published
publisher: Association for Computing Machinery
quality_controlled: '1'
scopus_import: '1'
status: public
title: 'Brief announcement: Be prepared when network goes bad: An asynchronous view-change
protocol'
type: conference
user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87
year: '2021'
...
---
OA_type: closed access
_id: '1315'
abstract:
- lang: eng
text: We prove optimal second order convergence of a modified lowest-order Brezzi-Douglas-Marini
(BDM1) mixed finite element scheme for advection-diffusion problems in divergence
form. If advection is present, it is known that the total flux is approximated
only with first-order accuracy by the classical BDM1 mixed method, which is suboptimal
since the same order of convergence is obtained if the computationally less expensive
Raviart-Thomas (RT0) element is used. The modification that was first proposed
by Brunner et al. [Adv. Water Res., 35 (2012),pp. 163-171] is based on the hybrid
problem formulation and consists in using the Lagrange multipliers for the discretization
of the advective term instead of the cellwise constant approximation of the scalar
unknown.
article_processing_charge: No
article_type: original
author:
- first_name: Fabian
full_name: Brunner, Fabian
last_name: Brunner
- first_name: Julian L
full_name: Fischer, Julian L
id: 2C12A0B0-F248-11E8-B48F-1D18A9856A87
last_name: Fischer
orcid: 0000-0002-0479-558X
- first_name: Peter
full_name: Knabner, Peter
last_name: Knabner
citation:
ama: Brunner F, Fischer JL, Knabner P. Analysis of a modified second-order mixed
hybrid BDM1 finite element method for transport problems in divergence form. Journal
on Numerical Analysis. 2016;54(4):2359-2378. doi:10.1137/15M1035379
apa: Brunner, F., Fischer, J. L., & Knabner, P. (2016). Analysis of a modified
second-order mixed hybrid BDM1 finite element method for transport problems in
divergence form. Journal on Numerical Analysis. Society for Industrial
and Applied Mathematics . https://doi.org/10.1137/15M1035379
chicago: Brunner, Fabian, Julian L Fischer, and Peter Knabner. “Analysis of a Modified
Second-Order Mixed Hybrid BDM1 Finite Element Method for Transport Problems in
Divergence Form.” Journal on Numerical Analysis. Society for Industrial
and Applied Mathematics , 2016. https://doi.org/10.1137/15M1035379.
ieee: F. Brunner, J. L. Fischer, and P. Knabner, “Analysis of a modified second-order
mixed hybrid BDM1 finite element method for transport problems in divergence form,”
Journal on Numerical Analysis, vol. 54, no. 4. Society for Industrial and
Applied Mathematics , pp. 2359–2378, 2016.
ista: Brunner F, Fischer JL, Knabner P. 2016. Analysis of a modified second-order
mixed hybrid BDM1 finite element method for transport problems in divergence form.
Journal on Numerical Analysis. 54(4), 2359–2378.
mla: Brunner, Fabian, et al. “Analysis of a Modified Second-Order Mixed Hybrid BDM1
Finite Element Method for Transport Problems in Divergence Form.” Journal on
Numerical Analysis, vol. 54, no. 4, Society for Industrial and Applied Mathematics
, 2016, pp. 2359–78, doi:10.1137/15M1035379.
short: F. Brunner, J.L. Fischer, P. Knabner, Journal on Numerical Analysis 54 (2016)
2359–2378.
date_created: 2018-12-11T11:51:19Z
date_published: 2016-08-02T00:00:00Z
date_updated: 2026-05-18T09:48:39Z
day: '02'
doi: 10.1137/15M1035379
extern: '1'
intvolume: ' 54'
issue: '4'
keyword:
- advection-diffusion problem
- mixed finite element methods
- suboptimal conver-gence
- optimal convergence
language:
- iso: eng
month: '08'
oa_version: None
page: 2359 - 2378
publication: Journal on Numerical Analysis
publication_identifier:
eissn:
- 1095-7170
issnl:
- 0036-1429
publication_status: published
publisher: 'Society for Industrial and Applied Mathematics '
publist_id: '5954'
quality_controlled: '1'
status: public
title: Analysis of a modified second-order mixed hybrid BDM1 finite element method
for transport problems in divergence form
type: journal_article
user_id: ba8df636-2132-11f1-aed0-ed93e2281fdd
volume: 54
year: '2016'
...