A finite element convergence analysis for 3D Stokes equations in case of variational crimes.
type: Item
instance of: scholarly article
title: A finite element convergence analysis for 3D Stokes equations in case of variational crimes.
zbMATH Open document ID: 1067.65129
DOI: 10.1023/A:1022235512626
published in: Applications of Mathematics
publication date: 2000-09-14T00:00:00Z
full work available at URL: https://eudml.org/doc/33051
review text: A Stokes problem with mixed boundary conditions is examined in a three-dimensional domain with a piecewise curved boundary. This domain is approximated by a polyhedron which is decomposed into tetrahedra. Then a nonconforming finite element method is applied. This leads to several variational crimes: numerical integration, approximation of the curved boundary, and boundary conditions. The author presents sufficient conditions which guarantee the convergence of discrete solutions to a weak solution of the Stokes problem without any additional regularity assumptions.
reviewed by: Michal Křížek
Mathematics Subject Classification ID: 65N30
Mathematics Subject Classification ID: 35Q30
zbMATH DE Number: 1508452
zbMATH Keywords: Stokes equations
zbMATH Keywords: nonstandard boundary conditions
zbMATH Keywords: finite element method
zbMATH Keywords: approximation of boundary
author: Petr Knobloch
MaRDI profile type: Publication
cites work: Mixed and Hybrid Finite Element Methods
cites work: Q3126804
cites work: Q5678400
cites work: On finite element approximations of problems having inhomogeneous essential boundary conditions
cites work: Finite element approximation of the Navier-Stokes equations
cites work: Q4335792
cites work: Q4261181
cites work: Q3094428
cites work: Q5607484
cites work: Q4404383
cites work: How to avoid the use of Green's theorem in the Ciarlet-Raviart theory of variational crimes
OpenAlex ID: W1517908999
Recommended article: Q4261181
Recommended article: Finite element analysis of variational crimes for a quasilinear elliptic problem in 3D
Recommended article: Q4372530
Recommended article: Finite element methods for the Stokes problem in \({\mathbb{R}}^3\)
Recommended article: Q3770162
Recommended article: Three-Dimensional Finite Element Methods for the Stokes Problem
Recommended article: Q4688844
Recommended article: Analysis on a finite volume element method for Stokes problems
Recommended article: Finite element methods for the Stokes system in three-dimensional exterior domains
Recommended article: Analysis of Some Finite Elements for the Stokes Problem
description: scientific article; zbMATH DE number 1508452