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Uniformly convergent adaptive methods for a class of parametric operator equations∗

Published online by Cambridge University Press:  13 June 2012

Claude Jeffrey Gittelson
Claude Jeffrey Gittelson*
Affiliation:
Seminar for Applied Mathematics, ETH Zurich, Rämistrasse 101, 8092 Zurich, Switzerland. claude.gittelson@sam.math.ethz.ch Department of Mathematics, Purdue University, 150 N. University Street, West Lafayette, 47907 IN, USA
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Abstract

We derive and analyze adaptive solvers for boundary value problems in which the differential operator depends affinely on a sequence of parameters. These methods converge uniformly in the parameters and provide an upper bound for the maximal error. Numerical computations indicate that they are more efficient than similar methods that control the error in a mean square sense.

Keywords

Parametric partial differential equationspartial differential equations with random coefficientsuniform convergenceadaptive methodsoperator equations
Type
Research Article
Information
ESAIM: Mathematical Modelling and Numerical Analysis , Volume 46 , Issue 6 , November 2012 , pp. 1485 - 1508
Copyright
© EDP Sciences, SMAI, 2012

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