Adaptive approximations for 3-D electrostatic plate problems
type: Item
instance of: scholarly article
title: Adaptive approximations for 3-D electrostatic plate problems
zbMATH Open document ID: 0769.65091
DOI: 10.1016/0965-9978(92)90102-L
published in: Advances in Engineering Software
publication date: 1993-06-29T00:00:00Z
review text: The charge density of a thin, electrified plate \(\Gamma\) loaded with a given potential is determined as the solution of a weakly singular integral equation. An approximate solution is found by the Galerkin scheme in a subspace of certain Sobolev spaces of distributions on \(\Gamma\). The space of piecewise constant functions of a grid of \(\Gamma\) is used, and the capacitance of the plate \(\Gamma\) is computed from the approximated charge density. In order to increase the convergence rate an adaptive method for the grid refinement is applied and two strategies are presented. The two refinement strategies are illustrated on two examples, where the domain is either a parallelogram or an \(L\)-shaped region.
Mathematics Subject Classification ID: 65Z05
Mathematics Subject Classification ID: 65N38
Mathematics Subject Classification ID: 65R20
Mathematics Subject Classification ID: 35Q60
Mathematics Subject Classification ID: 45E10
Mathematics Subject Classification ID: 78A30
zbMATH DE Number: 221755
zbMATH Keywords: 3-D electrostatic plate problems
zbMATH Keywords: finite elements
zbMATH Keywords: numerical results
zbMATH Keywords: boundary element Galerkin method
zbMATH Keywords: weakly singular integral equation
zbMATH Keywords: capacitance
zbMATH Keywords: convergence rate
zbMATH Keywords: adaptive method
zbMATH Keywords: grid refinement
Wikidata QID: Q56965235
author: V. J. Ervin
author: Ernst P. Stephan
MaRDI profile type: Publication
full work available at URL: 0965-9978(92)90102-l
OpenAlex ID: W2088234590
description: scientific article; zbMATH DE number 221755