The finite element method for a boundary value problem with strong singularity
type: Item
instance of: scholarly article
title: The finite element method for a boundary value problem with strong singularity
zbMATH Open document ID: 1194.65137
author: H. I. Rukavishnikova
author: Victor A. Rukavishnikov
published in: Journal of Computational and Applied Mathematics
publication date: 2010-06-22T00:00:00Z
review text: The paper deals with elliptic boundary value problems when the coefficients degenerate in the neighborhood of singular points. Weights in the Sobolev spaces are the remedy. There is some similarity with the use of weighted Sobolev spaces in the treatment of domains with reentrant corners.
reviewed by: D. Braess
Mathematics Subject Classification ID: 65N30
Mathematics Subject Classification ID: 35J25
Mathematics Subject Classification ID: 35J70
zbMATH DE Number: 5724554
zbMATH Keywords: elliptic equations with strong singularities
zbMATH Keywords: finite elements
zbMATH Keywords: Sobolev spaces
MaRDI profile type: Publication
full work available at URL: j.cam.2010.01.020
OpenAlex ID: W1976016743
cites work: Ritz–Galerkin Methods for Singular Boundary Value Problems
cites work: Galerkin Methods for Singular Boundary Value Problems in One Space Dimension
cites work: Error-bounds for finite element method
cites work: Finite element convergence for singular data
cites work: Improved Accuracy by Adapted Mesh-Refinements in the Finite Element Method
cites work: Finite Element Methods of Optimal Order for Problems with Singular Data
cites work: Mixed finite element approximation of a degenerate elliptic problem
cites work: Q5589570
cites work: Q3900390
cites work: Q3470840
cites work: Elliptic boundary value problems on corner domains. Smoothness and asymptotics of solutions
cites work: Numerical solution to the time-dependent Maxwell equations in two-dimensional singular domains: The singular complement method
cites work: EXPONENTIAL CONVERGENCE OF hp-FEM FOR MAXWELL EQUATIONS WITH WEIGHTED REGULARIZATION IN POLYGONAL DOMAINS
cites work: On the finite element method for elliptic problems with degenerate and singular coefficients
cites work: Analysis of a modified Schrödinger operator in 2D: Regularity, index, and FEM
cites work: Q3496602
cites work: Q4350235
cites work: On the uniqueness of the \(R_{\nu}\)-generalized solution of boundary value problems with noncoordinated degeneration of the initial data.
cites work: On the coercivity of the \(R_{v}\)-generalized solution of the first boundary value problem with coordinated degeneration of the input data
cites work: Coercive estimate for a boundary value problem with noncoordinated degeneration of the data
cites work: Q5689126
cites work: An exponential rate of convergence of the finite element method for the Dirichlet problem with a singularity of the solution.
cites work: Q5698709
cites work: Q3890207
cites work: The \(R_\nu \)-generalized solution of a boundary value problem with a singularity belongs to the space \(W_{2,\nu +\beta /2+\kappa +1}^{\kappa +2} (\Omega , \delta )\)
cites work: Q4169675
cites work: Q4758141
DOI: 10.1016/J.CAM.2010.01.020
description: scientific article; zbMATH DE number 5724554