Finite element error estimates for nonlinear elliptic equations of monotone type
type: Item
instance of: scholarly article
title: Finite element error estimates for nonlinear elliptic equations of monotone type
zbMATH Open document ID: 0643.65058
DOI: 10.1007/BF01396320
published in: Numerische Mathematik
publication date: 1989-01-01T00:00:00Z
full work available at URL: https://eudml.org/doc/133324
review text: We consider the application of the finite element method to a class of second order elliptic boundary value problems of divergence form and with gradient nonlinearity in the principal coefficient, and the derivation of error estimates for the finite element approximations. Such problems arise in many practical situations - for example, in shock-free airfoil design, seepage through coarse grained porous media, and in some glaciological problems. By making use of certain properties of the nonlinear coefficients, we demonstrate that the variational formulations associated with these boundary value problems are well-posed. We also prove that the abstract operators accompanying such problems satisfy certain continuity and monotonicity inequalities. With the aid of these inequalities and some standard results from approximation theory, we show how one may derive error estimates for the finite element approximations in the energy norm.
Mathematics Subject Classification ID: 65N15
Mathematics Subject Classification ID: 65N30
Mathematics Subject Classification ID: 35J65
zbMATH DE Number: 4048955
zbMATH Keywords: finite element method
zbMATH Keywords: second order elliptic boundary value problems of divergence form
zbMATH Keywords: gradient nonlinearity
zbMATH Keywords: error estimates
zbMATH Keywords: shock-free airfoil design
zbMATH Keywords: seepage through coarse grained porous media
zbMATH Keywords: glaciological problems
zbMATH Keywords: variational formulations
zbMATH Keywords: well-posed
zbMATH Keywords: continuity and monotonicity inequalities
zbMATH Keywords: energy norm
author: S. Chow
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 4048955