{"department":[{"_id":"JuFi"}],"type":"journal_article","abstract":[{"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.","lang":"eng"}],"article_type":"original","OA_type":"green","mathsc":["65N30","76D07","76M10"],"status":"public","date_published":"2026-08-04T00:00:00Z","title":"A Nitsche method for incompressible fluids with general dynamic boundary conditions","external_id":{"arxiv":["2502.09550"]},"author":[{"first_name":"Pablo Alexei","full_name":"Gazca-Orozco, Pablo Alexei","last_name":"Gazca-Orozco"},{"last_name":"Gmeineder","full_name":"Gmeineder, Franz","first_name":"Franz"},{"last_name":"Maringová","id":"dbabca31-66eb-11eb-963a-fb9c22c880b4","first_name":"Erika","full_name":"Maringová, Erika"},{"last_name":"Tscherpel","first_name":"Tabea","full_name":"Tscherpel, Tabea"}],"citation":{"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.","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>","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>","short":"P.A. Gazca-Orozco, F. Gmeineder, E. Maringová, T. Tscherpel, Mathematical Models and Methods in Applied Sciences (2026).","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>.","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>."},"user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","publisher":"World Scientific Publishing","oa_version":"Preprint","OA_place":"repository","doi":"10.1142/S0218202526500508","publication_status":"epub_ahead","oa":1,"publication":"Mathematical Models and Methods in Applied Sciences","month":"08","quality_controlled":"1","arxiv":1,"date_updated":"2026-08-18T07:51:59Z","date_created":"2026-08-16T22:01:44Z","year":"2026","main_file_link":[{"url":"https://doi.org/10.48550/arXiv.2502.09550","open_access":"1"}],"day":"04","_id":"22718","language":[{"iso":"eng"}],"publication_identifier":{"issn":["0218-2025"],"eissn":["1793-6314"]},"scopus_import":"1","article_processing_charge":"No"}