Superconvergent finite element solutions of Laplace and Poisson equation

Author

Franz, Jürgen ; Kasper, Manfred

Author_Institution

Technol. der Mikroperipherik, Tech. Univ. Berlin, Germany

Volume

32

Issue

3

fYear

1996

fDate

5/1/1996 12:00:00 AM

Firstpage

643

Lastpage

646

Abstract

The computation of local field quantities and forces is known to be one of the most serious problems in electromagnetic field computation. A novel technique for obtaining superconvergent derivatives of finite element solutions for Laplace and Poisson type equations is presented. This is achieved by analytical integration of Green´s function over single triangles. Superconvergent derivatives of FEM potential solutions have an accuracy of higher order than predicted by the finite element theory. Compared to direct evaluation the number of significant digits doubles. The procedure is illustrated by application to several test examples. It is notable that no restrictive regularity assumptions on the mesh topology are made

Keywords

Green´s function methods; Laplace equations; convergence of numerical methods; electromagnetic fields; finite element analysis; integration; stochastic processes; FEM potential solutions; Green´s function; Laplace equation; Poisson equation; analytical integration; electromagnetic field computation; finite element solutions; finite element theory; local field forces; local field quantities; mesh topology; superconvergent finite element solutions; triangles; Discrete Fourier transforms; Electromagnetic fields; Finite element methods; Fourier series; Green´s function methods; Laplace equations; Magnetic fields; Performance evaluation; Poisson equations; Testing; Topology;

fLanguage

English

Journal_Title

Magnetics, IEEE Transactions on

Publisher

ieee

ISSN

0018-9464

Type

jour

DOI

10.1109/20.497320

Filename

497320