Finite element approximation for some quasilinear elliptic problems
type: Item
instance of: scholarly article
title: Finite element approximation for some quasilinear elliptic problems
zbMATH Open document ID: 0951.65120
DOI: 10.1016/S0377-0427(98)00085-5
author: Yuki Matsuzawa
published in: Journal of Computational and Applied Mathematics
publication date: 2000-12-06T00:00:00Z
review text: The authors consider the finite element approximation of the boundary value problem \[ -\nabla\cdot(A(u)\nabla u) = f \quad \text{in } \Omega, \qquad u = 0 \quad \text{on } \partial\Omega. \] where \(\Omega\) is a two- or three-dimensional polyhedral domain and \(A(u)\) is a Lipschitz continuous function satisfying \(A(u)\geq\delta>0\). Under the assumption of the uniqueness of the weak solution, the authors can show the \(L^\infty\) convergence of the approximate solution.
Mathematics Subject Classification ID: 65N30
Mathematics Subject Classification ID: 65N12
Mathematics Subject Classification ID: 35J65
zbMATH DE Number: 1326428
zbMATH Keywords: quasilinear elliptic boundary value problem
zbMATH Keywords: finite element method
zbMATH Keywords: convergence
reviewed by: P. Neittaanmäki
MaRDI profile type: Publication
cites work: Q4300595
cites work: Q4748596
cites work: A Galerkin Method for a Nonlinear Dirichlet Problem
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description: scientific article; zbMATH DE number 1326428