Finite element approximation of a degenerating second-order elliptic equation in a domain with curvilinear boundary
type: Item
instance of: scholarly article
title: Finite element approximation of a degenerating second-order elliptic equation in a domain with curvilinear boundary
zbMATH Open document ID: 0822.65084
author: M. R. Timerbaev
published in: Russian Mathematics
publication date: 1995-05-17T00:00:00Z
review text: This paper is concerned with the solution of a boundary value problem for linear second-order elliptic equations degenerating on the boundary of the convex domain by the finite element method (FEM). The original problem is reduced to a variational one, the existence and the uniqueness for the solution of the variational problem were established earlier. Further the approximating family of solutions of FEM schemes for the problem is constructed using special domain triangulation collection condensing near the boundary and piecewise polynomial finite elements of arbitrary degree. The convergence of FEM schemes is studied, estimates for accuracy in terms of the regular mesh size and of the condensation degree are obtained. In the last section the author gives error bounds depending on the dimension of the approximating space.
reviewed by: Valery V. Kobkov
Mathematics Subject Classification ID: 65N30
Mathematics Subject Classification ID: 65N12
Mathematics Subject Classification ID: 65N15
Mathematics Subject Classification ID: 35J25
Mathematics Subject Classification ID: 35J70
zbMATH DE Number: 746059
zbMATH Keywords: degenerating elliptic problems
zbMATH Keywords: linear second-order elliptic equation
zbMATH Keywords: finite element method
zbMATH Keywords: domain triangulation
zbMATH Keywords: convergence
zbMATH Keywords: error bounds
MaRDI profile type: Publication
description: scientific article; zbMATH DE number 746059