Volume 46, Number 6, November-December 2012
|Page(s)||1485 - 1508|
|Published online||13 June 2012|
Uniformly convergent adaptive methods for a class of parametric operator equations∗
Seminar for Applied Mathematics, ETH Zurich,
Rämistrasse 101, 8092
2 Department of Mathematics, Purdue University, 150 N. University Street, West Lafayette, 47907 IN, USA
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
Current usage metrics show cumulative count of Article Views (full-text article views including HTML views, PDF and ePub downloads, according to the available data) and Abstracts Views on Vision4Press platform.
Data correspond to usage on the plateform after 2015. The current usage metrics is available 48-96 hours after online publication and is updated daily on week days.
Initial download of the metrics may take a while.