---
OA_place: repository
OA_type: green
_id: '22718'
abstract:
- lang: eng
  text: Both Newtonian and non-Newtonian fluids may exhibit complex slip behaviour
    at the boundary. We examine a broad class of slip boundary conditions that generalises
    the commonly used Navier slip, perfect slip, stick-slip and Tresca friction boundary
    conditions. In particular, set-valued, nonmonotone, noncoercive and dynamic relations
    may occur. For a unifying framework of such relations, we present a fully discrete
    numerical scheme for the time-dependent Navier–Stokes equations subject to impermeability
    and general slip-type boundary conditions on polyhedral domains. Based on compactness
    arguments, we prove convergence of subsequences, finally ensuring the existence
    of a weak solution. The numerical scheme uses a general inf-sup stable pair of
    finite element spaces for the velocity and pressure, a regularisation approach
    for the implicit slip boundary condition and, most importantly, a general Nitsche
    method to impose the impermeability and a backward Euler time stepping. One of
    the key tools in the convergence proof is an inhomogeneous Korn inequality that
    includes a normal trace term.
article_processing_charge: No
article_type: original
arxiv: 1
author:
- first_name: Pablo Alexei
  full_name: Gazca-Orozco, Pablo Alexei
  last_name: Gazca-Orozco
- first_name: Franz
  full_name: Gmeineder, Franz
  last_name: Gmeineder
- first_name: Erika
  full_name: Maringová, Erika
  id: dbabca31-66eb-11eb-963a-fb9c22c880b4
  last_name: Maringová
- first_name: Tabea
  full_name: Tscherpel, Tabea
  last_name: Tscherpel
citation:
  ama: Gazca-Orozco PA, Gmeineder F, Maringová E, Tscherpel T. A Nitsche method for
    incompressible fluids with general dynamic boundary conditions. <i>Mathematical
    Models and Methods in Applied Sciences</i>. 2026. doi:<a href="https://doi.org/10.1142/S0218202526500508">10.1142/S0218202526500508</a>
  apa: Gazca-Orozco, P. A., Gmeineder, F., Maringová, E., &#38; Tscherpel, T. (2026).
    A Nitsche method for incompressible fluids with general dynamic boundary conditions.
    <i>Mathematical Models and Methods in Applied Sciences</i>. World Scientific Publishing.
    <a href="https://doi.org/10.1142/S0218202526500508">https://doi.org/10.1142/S0218202526500508</a>
  chicago: Gazca-Orozco, Pablo Alexei, Franz Gmeineder, Erika Maringová, and Tabea
    Tscherpel. “A Nitsche Method for Incompressible Fluids with General Dynamic Boundary
    Conditions.” <i>Mathematical Models and Methods in Applied Sciences</i>. World
    Scientific Publishing, 2026. <a href="https://doi.org/10.1142/S0218202526500508">https://doi.org/10.1142/S0218202526500508</a>.
  ieee: P. A. Gazca-Orozco, F. Gmeineder, E. Maringová, and T. Tscherpel, “A Nitsche
    method for incompressible fluids with general dynamic boundary conditions,” <i>Mathematical
    Models and Methods in Applied Sciences</i>. World Scientific Publishing, 2026.
  ista: Gazca-Orozco PA, Gmeineder F, Maringová E, Tscherpel T. 2026. A Nitsche method
    for incompressible fluids with general dynamic boundary conditions. Mathematical
    Models and Methods in Applied Sciences.
  mla: Gazca-Orozco, Pablo Alexei, et al. “A Nitsche Method for Incompressible Fluids
    with General Dynamic Boundary Conditions.” <i>Mathematical Models and Methods
    in Applied Sciences</i>, World Scientific Publishing, 2026, doi:<a href="https://doi.org/10.1142/S0218202526500508">10.1142/S0218202526500508</a>.
  short: P.A. Gazca-Orozco, F. Gmeineder, E. Maringová, T. Tscherpel, Mathematical
    Models and Methods in Applied Sciences (2026).
date_created: 2026-08-16T22:01:44Z
date_published: 2026-08-04T00:00:00Z
date_updated: 2026-08-18T07:51:59Z
day: '04'
department:
- _id: JuFi
doi: 10.1142/S0218202526500508
external_id:
  arxiv:
  - '2502.09550'
language:
- iso: eng
main_file_link:
- open_access: '1'
  url: https://doi.org/10.48550/arXiv.2502.09550
mathsc:
- 65N30
- 76D07
- 76M10
month: '08'
oa: 1
oa_version: Preprint
publication: Mathematical Models and Methods in Applied Sciences
publication_identifier:
  eissn:
  - 1793-6314
  issn:
  - 0218-2025
publication_status: epub_ahead
publisher: World Scientific Publishing
quality_controlled: '1'
scopus_import: '1'
status: public
title: A Nitsche method for incompressible fluids with general dynamic boundary conditions
type: journal_article
user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87
year: '2026'
...