| Issue |
ESAIM: M2AN
Volume 46, Number 6, November-December 2012
|
|
|---|---|---|
| Page(s) | 1485 - 1508 | |
| DOI | https://doi.org/10.1051/m2an/2012013 | |
| Published online | 13 June 2012 | |
Uniformly convergent adaptive methods for a class of parametric operator equations∗
1
Seminar for Applied Mathematics, ETH Zurich,
Rämistrasse 101, 8092
Zurich,
Switzerland
claude.gittelson@sam.math.ethz.ch
2
Department of Mathematics, Purdue University,
150 N. University Street,
West Lafayette, 47907
IN,
USA
Received:
20
March
2012
Revised:
16
October
2011
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.
Mathematics Subject Classification: 35R60 / 47B80 / 65C20 / 65N12 / 65N22 / 65J10
Key words: Parametric partial differential equations / partial differential equations with random coefficients / uniform convergence / adaptive methods / operator equations
© EDP Sciences, SMAI, 2012
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