Skip to Main Content

Mathematics of Computation

Published by the American Mathematical Society since 1960 (published as Mathematical Tables and other Aids to Computation 1943-1959), Mathematics of Computation is devoted to research articles of the highest quality in computational mathematics.

ISSN 1088-6842 (online) ISSN 0025-5718 (print)

The 2020 MCQ for Mathematics of Computation is 1.78.

What is MCQ? The Mathematical Citation Quotient (MCQ) measures journal impact by looking at citations over a five-year period. Subscribers to MathSciNet may click through for more detailed information.

 

An adaptive stochastic Galerkin method for random elliptic operators
HTML articles powered by AMS MathViewer

by Claude Jeffrey Gittelson
Math. Comp. 82 (2013), 1515-1541
DOI: https://doi.org/10.1090/S0025-5718-2013-02654-3
Published electronically: February 12, 2013

Abstract:

We derive an adaptive solver for random elliptic boundary value problems, using techniques from adaptive wavelet methods. Substituting wavelets by polynomials of the random parameters leads to a modular solver for the parameter dependence of the random solution, which combines with any discretization on the spatial domain. In addition to selecting active polynomial modes, this solver can adaptively construct a separate spatial discretization for each of their coefficients. We show convergence of the solver in this general setting, along with a computable bound for the mean square error, and an optimality property in the case of a single spatial discretization. Numerical computations demonstrate convergence of the solver and compare it to a sparse tensor product construction.
References
Similar Articles
Bibliographic Information
  • Claude Jeffrey Gittelson
  • Affiliation: Seminar for Applied Mathematics, ETH Zurich, Rämistrasse 101, CH-8092 Zurich, Switzerland
  • Address at time of publication: Department of Mathematics, Purdue University, 150 N. University Street, West Lafayette, Indiana 47907
  • Email: cgittels@purdue.edu
  • Received by editor(s): March 2, 2011
  • Received by editor(s) in revised form: September 24, 2011
  • Published electronically: February 12, 2013
  • Additional Notes: This research was supported in part by the Swiss National Science Foundation grant No. 200021-120290/1.
  • © Copyright 2013 American Mathematical Society
    The copyright for this article reverts to public domain 28 years after publication.
  • Journal: Math. Comp. 82 (2013), 1515-1541
  • MSC (2010): Primary 35R60, 47B80, 60H25, 65C20, 65N12, 65N22, 65N30, 65J10, 65Y20
  • DOI: https://doi.org/10.1090/S0025-5718-2013-02654-3
  • MathSciNet review: 3042573