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Uniformly convergent adaptive methods for a class of parametricoperator 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. [email protected] 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 thedifferential operator depends affinely on a sequence of parameters. These methods convergeuniformly in the parameters and provide an upper bound for the maximal error. Numericalcomputations indicate that they are more efficient than similar methods that control theerror 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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