On the finite element-least squares approximation to higher order elliptic systems
type: Item
instance of: scholarly article
title: On the finite element-least squares approximation to higher order elliptic systems
zbMATH Open document ID: 0597.65082
DOI: 10.1007/BF00276860
published in: Archive for Rational Mechanics and Analysis
publication date: 1985-01-01T00:00:00Z
review text: The paper deals with the least square approximation of the biharmonic equation with homogeneous Dirichlet boundary conditions. The problem is transformed into the first order system for variables \(\phi_ 0,u_ 0,\phi_ 1,u_ 1\), where \(\phi_ 0\) is the solution of the original biharmonic problem, \(u_ 0=\nabla \phi_ 0\), \(\phi_ 1=\Delta \phi_ 0\), \(u_ 1=\text{grad} \Delta \phi_ 0\) (the generalization to the \(2m^{th}\) order case is given in the last section). The first order system is then solved by means of the least squares method over suitable finite element spaces. Error estimates in appropriate norms for all above listed variables are derived. The theory presented in the paper holds under the standard regularity assumptions (data as well as the domain are smooth).
Mathematics Subject Classification ID: 65N30
Mathematics Subject Classification ID: 65N15
Mathematics Subject Classification ID: 35J40
zbMATH DE Number: 3963138
zbMATH Keywords: least square approximation
zbMATH Keywords: biharmonic equation
zbMATH Keywords: finite element
zbMATH Keywords: Error estimates
author: George J. Fix
author: Ernst P. Stephan
MaRDI profile type: Publication
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full work available at URL: https://doi.org/10.1007/bf00276860
OpenAlex ID: W4249802338
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description: scientific article; zbMATH DE number 3963138