Optimal \(L^{\infty}\)-error estimates for piecewise linear finite elements in \({\mathbb{R}}^ n\) for 1\(\leq n\leq 3\)
type: Item
instance of: scholarly article
title: Optimal \(L^{\infty}\)-error estimates for piecewise linear finite elements in \({\mathbb{R}}^ n\) for 1\(\leq n\leq 3\)
zbMATH Open document ID: 0589.65071
DOI: 10.1007/BF01390711
author: Ludwig Kohaupt
published in: Numerische Mathematik
publication date: 1987-01-01T00:00:00Z
full work available at URL: https://eudml.org/doc/133159
review text: For two second order elliptic boundary value problems, uniform convergence error estimates are derived using piecewise linear (conforming and non-conforming) finite elements. The estimates are valid for polyhedral convex regions \(\Omega \subset \mathbb{R}^ n\) with \(1\leq n\leq 3\). The proof of the estimates is mainly based on Sobolev's inequality, by which the uniform estimates are reduced to estimates in the mean. In this way, it is possible to obtain the desired uniform estimate \(O(h^ 2)\) in the plane as a special case, thus conforming theoretically Natterer's numerical results.
Mathematics Subject Classification ID: 65N15
Mathematics Subject Classification ID: 65N30
Mathematics Subject Classification ID: 35J25
zbMATH DE Number: 3947561
zbMATH Keywords: uniform convergence error estimates
zbMATH Keywords: finite elements
zbMATH Keywords: Sobolev's inequality
MaRDI profile type: Publication
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OpenAlex ID: W4253449038
description: scientific article; zbMATH DE number 3947561