Anisotropic mesh refinement in stabilized Galerkin methods
type: Item
instance of: scholarly article
title: Anisotropic mesh refinement in stabilized Galerkin methods
zbMATH Open document ID: 0878.65097
author: Thomas Apel
author: Gert Lube
published in: Numerische Mathematik
publication date: 1997-10-20T00:00:00Z
full work available at URL: urn:nbn:de:bsz:ch1-199800640
review text: This paper is concerned with the finite element solution of the following elliptic boundary value problem in a bounded polyhedral domain \( \Omega \subseteq\mathbb{R}^d, d=2,3\), with Lipschitz boundary \( \partial \Omega \): \[ -\epsilon \Delta u+b\cdot\nabla u+c u=f\quad \text{in} \Omega,\quad u=0 \quad \text{on} \partial\Omega, \] \(\epsilon \in (0,1]\) is a parameter. The aim is to extend the numerical analysis of the Galerkin/least squares methods to meshes which are anisotropically refined at least in the boundary layers to derive error estimates in the energy norm uniformly with respect to \( \epsilon \in (0,1] \). At the end an application to problems of channel type is presented.
Mathematics Subject Classification ID: 65N30
Mathematics Subject Classification ID: 65N50
Mathematics Subject Classification ID: 35J25
zbMATH DE Number: 932029
zbMATH Keywords: elliptic boundary value problems
zbMATH Keywords: Galerkin finite element methods
zbMATH Keywords: anisotropic mesh refinement
reviewed by: Ariadna Lucia Pletea
MaRDI profile type: Publication
OpenAlex ID: W1994497771
DOI: 10.1007/S002110050216
description: scientific article; zbMATH DE number 932029