An approach for combining the Ritz-Galerkin and finite element method
type: Item
instance of: scholarly article
title: An approach for combining the Ritz-Galerkin and finite element method
zbMATH Open document ID: 0541.65069
DOI: 10.1016/0021-9045(83)90087-4
published in: Journal of Approximation Theory
publication date: 1983-01-01T00:00:00Z
review text: A combined method for solving the two dimensional elliptic model problem \[ -\partial /\partial x(\beta \partial u/\partial x)-\partial /\partial y(\beta \partial u/\partial y)=f,\quad(x,y)\in s;\quad u=g,\quad(x,y)\in \Gamma \] which has been widely used is studied. The combined method consists in dividing s by a circle \(\Gamma_ 0\) into 2 subdomains: a circular domain \(s_ 2\) contained in s and another domain \(s_ 1\) such that \(s=s_ 1+s_ 2\). Two quite different methods, the finite element method and the Ritz-Galerkin method, are used on \(s_ 1\) and \(s_ 2\), respectively. The use of combined methods is particularly important in problems with complicated boundaries or boundary conditions, or in problems with solutions which are not smooth enough or have singularities or in problems with unbounded solution domains. In such cases, a single method is often ineffective. This method has the advantages that it is valid for general nonhomogeneous elliptic boundary value problems and that it is reasonably simple to describe.
Mathematics Subject Classification ID: 65N30
Mathematics Subject Classification ID: 65N15
Mathematics Subject Classification ID: 35J25
zbMATH DE Number: 3860336
zbMATH Keywords: unbounded domains
zbMATH Keywords: combined method
zbMATH Keywords: finite element method
zbMATH Keywords: Ritz-Galerkin method
zbMATH Keywords: singularities
author: Zi-Cai Li
reviewed by: Sanming Zhou
MaRDI profile type: Publication
full work available at URL: 0021-9045(83)90087-4
OpenAlex ID: W2042699866
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description: scientific article; zbMATH DE number 3860336