A parallel Newton multigrid method for high order finite elements and its application on numerical existence proofs for elliptic boundary value equations

Wieners, Christian (1996) A parallel Newton multigrid method for high order finite elements and its application on numerical existence proofs for elliptic boundary value equations.
Published in: Zeitschrift für Angewandte Mathematik und Mechanik Vol. 76 (3). pp. 175-180.

Abstract

We describe a parallel algorithm for the numerical computation of guaranteed bounds for solutions of elliptic boundary value equations of second order. We use C 2 -Hermite-elements and a parallel Newton multigrid method to produce approximations of high accuracy. Then, we compute upper bounds for the defect and enclosures for the eigenvalues of the linearization. In order to obtain verified bounds, these computations are realized in interval arithmetic. The application of the Newton-Kantorovich-theorem yields the existence of a solution and error bounds for the approximation. The method is implemented on a 256 processor transputer grid and tested for the Bratu problem -Delta u=lambdaexp(u).


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Deposit Information:
ZAIK Number: zpr94-177
Depositing User: Archive Admin
Date Deposited: 02 Apr 2001 00:00
Last Modified: 19 Dec 2011 09:46
URI: http://e-archive.informatik.uni-koeln.de/id/eprint/177