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We discretize a tangential tensor field equation using a surface-finite element approach with a penalization term to ensure almost tangentiality. It is natural to measure the quality of such a discretization intrinsically, i.e., to examine…

Numerical Analysis · Mathematics 2022-05-26 Hanne Hardering , Simon Praetorius

In this paper, we propose a new approach -- the Tempered Finite Element Method (TFEM) -- that extends the Finite Element Method (FEM) to classes of meshes that include zero-measure or nearly degenerate elements for which standard FEM…

Numerical Analysis · Mathematics 2024-11-27 Antoine Quiriny , Václav Kučera , Jonathan Lambrechts , Nicolas Moës , Jean-François Remacle

We study a fictitious domain approach with Lagrange multipliers to discretize Stokes equations on a mesh that does not fit the boundaries. A mixed finite element method is used for fluid flow. Several stabilization terms are added to…

Numerical Analysis · Mathematics 2017-10-24 Michel Fournié , Alexei Lozinski

In this paper we propose and analyze a new Finite Element method for the solution of the two- and three-dimensional incompressible Navier--Stokes equations based on a hybrid discretization of both the velocity and pressure variables. The…

In this paper we study finite element discretizations of a surface vector-Laplace eigenproblem. We consider two known classes of finite element methods, namely one based on a vector analogon of the Dziuk-Elliott surface finite element…

Numerical Analysis · Mathematics 2020-11-06 Arnold Reusken

We present and analyze a linearized finite element method (FEM) for the dynamical incompressible magnetohydrodynamics (MHD) equations. The finite element approximation is based on mixed conforming elements, where Taylor--Hood type elements…

Numerical Analysis · Mathematics 2019-02-20 Huadong Gao , Weifeng Qiu

In this paper, a stabilized extended finite element method is proposed for Stokes interface problems on unfitted triangulation elements which do not require the interface align with the triangulation. The velocity solution and pressure…

Numerical Analysis · Mathematics 2021-01-19 Xiaoxiao He , Fei Song , Weibing Deng

We present a new high order finite element method for the discretization of partial differential equations on stationary smooth surfaces which are implicitly described as the zero level of a level set function. The discretization is based…

Numerical Analysis · Mathematics 2017-04-17 Jörg Grande , Christoph Lehrenfeld , Arnold Reusken

We consider the P1/P1 or P1b/P1 finite element approximations to the Stokes equations in a bounded smooth domain subject to the slip boundary condition. A penalty method is applied to address the essential boundary condition $u\cdot n = g$…

Numerical Analysis · Mathematics 2015-05-26 Takahito Kashiwabara , Issei Oikawa , Guanyu Zhou

We introduce a surface finite element method for the numerical solution of Navier-Stokes equations on evolving surfaces with a prescribed deformation of the surface in normal direction. The method is based on approaches for the full surface…

Numerical Analysis · Mathematics 2023-06-16 Veit Krause , Eric Kunze , Axel Voigt

Piecewise divergence-free nonconforming virtual elements are designed for Stokes problem in any dimensions. After introducing a local energy projector based on the Stokes problem and the stabilization, a divergence-free nonconforming…

Numerical Analysis · Mathematics 2021-03-22 Huayi Wei , Xuehai Huang , Ao Li

Stability and error analysis of a hybridized discontinuous Galerkin finite element method for Stokes equations is presented. The method is locally conservative, and for particular choices of spaces the velocity field is point-wise…

Numerical Analysis · Mathematics 2018-02-01 Sander Rhebergen , Garth N. Wells

The Stokes equations subject to non-homogeneous slip boundary conditions are considered in a smooth domain $\Omega \subset \mathbb R^N \, (N=2,3)$. We propose a finite element scheme based on the nonconforming P1/P0 approximation…

Numerical Analysis · Mathematics 2018-09-26 Takahito Kashiwabara , Issei Oikawa , Guanyu Zhou

This work introduces a stabilised finite element formulation for the Stokes flow problem with a nonlinear slip boundary condition of friction type. The boundary condition is enforced with the help of an additional Lagrange multiplier and…

Numerical Analysis · Mathematics 2024-05-21 Tom Gustafsson , Juha Videman

Super-convergence of order 1.5 in pressure and velocity has been experimentally investigated for the two-dimensional Stokes problem discretised with the MINI mixed finite element. Even though the classic mixed finite element theory for the…

Numerical Analysis · Mathematics 2019-01-04 Andrea Cioncolini , Daniele Boffi

This paper studies the stability of velocity-pressure mixed approximations of the Stokes problem when different finite element (FE) spaces for each component of the velocity field are considered. We consider some new combinations of…

Numerical Analysis · Mathematics 2014-12-01 F. Guillén González , J. R. Rodríguez Galván

An efficient and accurate finite-element algorithm is described for the numerical solution of the incompressible Navier-Stokes (INS) equations. The new algorithm that solves the INS equations in a velocity-pressure reformulation is based on…

Numerical Analysis · Mathematics 2020-02-19 Longfei Li

We develop a cut finite element method for the Darcy problem on surfaces. The cut finite element method is based on embedding the surface in a three dimensional finite element mesh and using finite element spaces defined on the three…

Numerical Analysis · Mathematics 2017-10-11 Peter Hansbo , Mats G. Larson , Andre Massing

This article focusses on the analysis of a conforming finite element method for the time-dependent incompressible Navier-Stokes equations. For divergence-free approximations, in a semi-discrete formulation, we prove error estimates for the…

Numerical Analysis · Mathematics 2018-03-20 Philipp W. Schroeder , Gert Lube

In this paper we analyze the finite element approximation of the Stokes equations with non-smooth Dirichlet boundary data. To define the discrete solution, we first approximate the boundary datum by a smooth one and then apply a standard…

Numerical Analysis · Mathematics 2019-12-12 Ricardo G. Durán , Lucia Gastaldi , Ariel L. Lombardi