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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.

 

A randomized and fully discrete Galerkin finite element method for semilinear stochastic evolution equations
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by Raphael Kruse and Yue Wu HTML | PDF
Math. Comp. 88 (2019), 2793-2825 Request permission

Abstract:

In this paper the numerical solution of nonautonomous semilinear stochastic evolution equations driven by an additive Wiener noise is investigated. We introduce a novel fully discrete numerical approximation that combines a standard Galerkin finite element method with a randomized Runge–Kutta scheme. Convergence of the method to the mild solution is proven with respect to the $L^p$-norm, $p \in [2,\infty )$. We obtain the same temporal order of convergence as for Milstein–Galerkin finite element methods but without imposing any differentiability condition on the nonlinearity. The results are extended to also incorporate a spectral approximation of the driving Wiener process. An application to a stochastic partial differential equation is discussed and illustrated through a numerical experiment.
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Additional Information
  • Raphael Kruse
  • Affiliation: Institut für Mathematik, Technische Universität Berlin, Secr. MA 5-3, Straße des 17. Juni 136, DE-10623 Berlin, Germany
  • MR Author ID: 904215
  • Email: kruse@math.tu-berlin.de
  • Yue Wu
  • Affiliation: Institut für Mathematik, Technische Universität Berlin, Secr. MA 5-3, Straße des 17. Juni 136, DE-10623 Berlin, Germany
  • MR Author ID: 1161278
  • Email: wu@math.tu-berlin.de
  • Received by editor(s): January 28, 2018
  • Received by editor(s) in revised form: December 5, 2018
  • Published electronically: March 26, 2019
  • Additional Notes: The authors gratefully acknowledge financial support by the German Research Foundation through the research unit FOR 2402 – Rough paths, stochastic partial differential equations and related topics – at TU Berlin.
  • © Copyright 2019 American Mathematical Society
  • Journal: Math. Comp. 88 (2019), 2793-2825
  • MSC (2010): Primary 65C30; Secondary 60H15, 65M12, 65M60
  • DOI: https://doi.org/10.1090/mcom/3421
  • MathSciNet review: 3985476