Penalty combinations of the Ritz-Galerkin and finite difference methods for singularity problems
type: Item
instance of: scholarly article
title: Penalty combinations of the Ritz-Galerkin and finite difference methods for singularity problems
zbMATH Open document ID: 0886.65106
DOI: 10.1016/S0377-0427(96)00148-3
author: O. Diekmann
published in: Journal of Computational and Applied Mathematics
publication date: 1998-04-20T00:00:00Z
review text: It is well known that incorporation of singular functions in the basis of the approximating subspace may greatly improve the accuracy of the finite element method [see results and references in the reviewer's book: Optimization in solving elliptic problems (1996; Zbl 0852.65087)]. In this paper, special attention is paid to a similar combination of difference methods (in \(S_1\)) and projective methods (in \(S_2\)), where \(\overline S_1\) and \(\overline S_2\) form a partition of the original region \(\overline S\) and \(\overline S_2\) contains a singular point. The coupling is done via a special penalty method on the cutting line \(\partial S_1\cap\partial S_2\). Estimates of type \(O(h^{3/2})\) are proved for a grid norm. Numerical experiments for a model problem are presented but the accuracy of approximations is not very high.
Mathematics Subject Classification ID: 65N06
Mathematics Subject Classification ID: 65N15
Mathematics Subject Classification ID: 65N30
Mathematics Subject Classification ID: 35J25
zbMATH DE Number: 1043096
zbMATH Keywords: combined methods
zbMATH Keywords: error bounds
zbMATH Keywords: Ritz-Galerkin method
zbMATH Keywords: numerical experiments
zbMATH Keywords: singular functions
zbMATH Keywords: finite element method
zbMATH Keywords: difference methods
zbMATH Keywords: projective methods
zbMATH Keywords: penalty method
reviewed by: Evgeniĭ Dyakonov
MaRDI profile type: Publication
cites work: On the Accuracy of the Finite Volume Element Method for Diffusion Equations on Composite Grids
cites work: The Finite Volume Element Method for Diffusion Equations on General Triangulations
cites work: Superconvergence phenomenon in the finite element method arising from averaging gradients
cites work: On a global superconvergence of the gradient of linear triangular elements
cites work: An approach combining the Ritz‐Galerkin and finite difference methods
cites work: Penalty-combined approaches to the Ritz-Galerkin and finite element methods for singularity problems of elliptic equations
cites work: Nodal Superconvergence and Solution Enhancement for a Class of Finite-Element and Finite-Difference Methods
cites work: Superconvergence of the gradient of Galerkin approximations for elliptic problems
cites work: Superconvergence analysis of approximate boundary-flux calculations
cites work: Q5248969
cites work: Q3993078
cites work: Q3126803
cites work: Superconvergent recovery of gradients on subdomains from piecewise linear finite‐element approximations
description: scientific article; zbMATH DE number 1043096