Determination of the modulus of quadrilaterals by finite element methods
type: Item
instance of: scholarly article
title: Determination of the modulus of quadrilaterals by finite element methods
zbMATH Open document ID: 0707.30005
author: Heihachiro Hara
author: Hisao Mizumoto
published in: Journal of the Mathematical Society of Japan
publication date: 1990-01-01T00:00:00Z
review text: The aim of the paper is to establish a method of finite element approximations by which the modulus of quadrilaterals on Riemann surfaces can be determined. The boundary of the quadrilateral Q is supposed to be compact and piecewise analytic. The characteristic of the method is the use of ordinary triangular meshes and linear elements on parametric disks that are mapped on subregions of Q. The corresponding approximating functions satisfy the boundary conditions exactly even in the case of curvilinear boundary arcs, and express singular property exactly near inner and corner singularities. This results in optimal error bounds (e.g. \(O(h^ 2)\) for the modulus of Q). Since these comparable approximations are hard to compute a class of modified approximating functions is introduced. It is shown that this modification does not change the order of convergence. Numerical calculations of the modulus of some concrete quadrilaterals show fairly good results also for the case of plane domains.
Mathematics Subject Classification ID: 30C30
Mathematics Subject Classification ID: 65N30
zbMATH DE Number: 4161048
zbMATH Keywords: Riemann surfaces
reviewed by: J. Weisel
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.2969/jmsj/04220295
OpenAlex ID: W2075357853
DOI: 10.2969/JMSJ/04220295
description: scientific article; zbMATH DE number 4161048