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We present a domain decomposition formulation based on hybridization which is inspired by hybridized discontinuous Galerkin (HDG) methods, that enhance mixed domain decomposition methods by incorporating stabilization terms. Unlike…

Numerical Analysis · Mathematics 2026-04-27 Kersten Schmidt , Timon Seibel , Sebastian Schöps

In this article we obtain an optimal best approximation type result for fully discrete approximations of the transient Stokes problem. For the time discretization we use the discontinuous Galerkin method and for the spatial discretization…

Numerical Analysis · Mathematics 2021-07-26 Niklas Behringer , Dmitriy Leykekhman , Boris Vexler

The paper develops and analyzes a higher-order unfitted finite element method for the incompressible Stokes equations, which yields a strongly divergence-free velocity field up to the physical boundary. The method combines an isoparametric…

Numerical Analysis · Mathematics 2025-12-16 Michael Neilan , Maxim Olshanskii , Henry von Wahl

Within the last years pressure robust methods for the discretization of incompressible fluids have been developed. These methods allow the use of standard finite elements for the solution of the problem while simultaneously removing a…

Numerical Analysis · Mathematics 2022-09-20 Seshadri R. Basava , Winnifried Wollner

We present optimal preconditioners for a recently introduced hybridized discontinuous Galerkin finite element discretization of the Stokes equations. Typical of hybridized discontinuous Galerkin methods, the method has degrees-of-freedom…

Numerical Analysis · Mathematics 2023-07-06 Sander Rhebergen , Garth N. Wells

We present analysis of two lowest-order hybridizable discontinuous Galerkin methods for the Stokes problem, while making only minimal regularity assumptions on the exact solution. The methods under consideration have previously been shown…

Numerical Analysis · Mathematics 2023-07-07 Aaron Baier-Reinio , Sander Rhebergen , Garth N. Wells

This paper presents a pressure-robust and element-wise divergence-free nonconforming finite element method for the Stokes problem on curved domains. The discrete element is constructed by mapping the Fortin-Soulie element from a reference…

Numerical Analysis · Mathematics 2026-04-15 Wei Chen , Zhen Liu

In this paper, we propose a new formulation and a suitable finite element method for the steady coupling of viscous flow in deformable porous media using divergence-conforming filtration fluxes. The proposed method is based on the use of…

Numerical Analysis · Mathematics 2025-10-23 Ruben Caraballo , Chansophea Wathanak In , Alberto F. Martín , Ricardo Ruiz-Baier

In this study, we investigate an anisotropic weakly over-penalised symmetric interior penalty method for the Stokes equation {on convex domains}. Our approach is a simple discontinuous Galerkin method similar to the Crouzeix--Raviart finite…

Numerical Analysis · Mathematics 2024-04-08 Hiroki Ishizaka

In the present work, we propose to extend to the Stokes problem a fictitious domain approach inspired by eXtended Finite Element Method and studied for Poisson problem in [Renard]. The method allows computations in domains whose boundaries…

Numerical Analysis · Mathematics 2015-06-15 Sébastien Court , Michel Fournié , Alexei Lozinski

We introduce new control-volume finite-element discretization schemes suitable for solving the Stokes problem. Within a common framework, we present different approaches for constructing such schemes. The first and most established strategy…

Numerical Analysis · Mathematics 2025-02-05 Martin Schneider , Timo Koch

This paper is concerned with fully discrete mixed finite element approximations of the time-dependent stochastic Stokes equations with multiplicative noise. A prototypical method, which comprises of the Euler-Maruyama scheme for time…

Numerical Analysis · Mathematics 2020-04-28 Xiaobing Feng , Hailong Qiu

In this paper, we propose and analyze an abstract stabilized mixed finite element framework that can be applied to nonlinear incompressible elasticity problems. In the abstract stabilized framework, we prove that any mixed finite element…

Numerical Analysis · Mathematics 2020-07-30 Qingguo Hong , Chunmei Liu , Jinchao Xu

The Stokes system with constant viscosity can be cast into different formulations by exploiting the incompressibility constraint. For instance the strain in the weak formulation can be replaced by the gradient to decouple the velocity…

Numerical Analysis · Mathematics 2016-04-28 Markus Huber , Ulrich Rüde , Christian Waluga , Barbara Wohlmuth

In this paper, for the generalized Darcy problem (an elliptic equation with discontinuous coefficients), we study a special partial Least-Squares (Galerkin-least-squares) method, known as the augmented mixed finite element method, and its…

Numerical Analysis · Mathematics 2023-12-29 Yuxiang Liang , Shun Zhang

We propose a new discretization method for the Stokes equations. The method is an improved version of the method recently presented in [C. Lehrenfeld, J. Sch\"oberl, Comp. Meth. Appl. Mech. Eng., 361 (2016)] which is based on an…

Numerical Analysis · Mathematics 2018-03-29 Philip L. Lederer , Christoph Lehrenfeld , Joachim Schöberl

We study a finite element approximation of a coupled fluid-structure interaction consisting of a three-dimensional incompressible viscous fluid governed by the unsteady Stokes equations and a two-dimensional elastic plate. To avoid the use…

Numerical Analysis · Mathematics 2026-02-10 Lander Besabe , Hyesuk Lee

In this thesis, we investigate a novel local projection based stabilized conforming virtual element method for the generalized Oseen problem using equal-order element pairs on general polygonal meshes. To ensure the stability, particularly…

Numerical Analysis · Mathematics 2025-09-05 Sudheer Mishra , E Natarajan

The aim of this paper is to propose a systematic way to obtain convergent finite element schemes for the Darcy-Stokes flow problem by combining well-known mixed finite elements that are separately convergent for Darcy and Stokes problems.…

Numerical Analysis · Mathematics 2012-03-22 Antonio Márquez , Salim Meddahi , Francisco-Javier Sayas

We present an isoparametric unfitted finite element approach of the CutFEM or Nitsche-XFEM family for the simulation of two-phase Stokes problems with slip between phases. For the unfitted generalized Taylor--Hood finite element pair…

Numerical Analysis · Mathematics 2021-01-26 Maxim Olshanskii , Annalisa Quaini , Qi Sun