Overview
- Employing Galerkin finite element methods closes the gap between theoretical convergence results and standard PDE solvers in widely used software packages
- Derives the optimal order of strong convergence through optimal regularity results
- Includes a self-contained introduction to Malliavin calculus
- Effectively approaches weak convergence for SPDEs with stochastic coefficients by avoiding Kolmogorov’s backward equation
- Includes supplementary material: sn.pub/extras
Part of the book series: Lecture Notes in Mathematics (LNM, volume 2093)
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Table of contents (6 chapters)
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Front Matter
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Back Matter
Keywords
About this book
In this book we analyze the error caused by numerical schemes for the approximation of semilinear stochastic evolution equations (SEEq) in a Hilbert space-valued setting. The numerical schemes considered combine Galerkin finite element methods with Euler-type temporal approximations. Starting from a precise analysis of the spatio-temporal regularity of the mild solution to the SEEq, we derive and prove optimal error estimates of the strong error of convergence in the first part of the book.
The second part deals with a new approach to the so-called weak error of convergence, which measures the distance between the law of the numerical solution and the law of the exact solution. This approach is based on Bismut’s integration by parts formula and the Malliavin calculus for infinite dimensional stochastic processes. These techniques are developed and explained in a separate chapter, before the weak convergence is proven for linear SEEq.
Authors and Affiliations
Bibliographic Information
Book Title: Strong and Weak Approximation of Semilinear Stochastic Evolution Equations
Authors: Raphael Kruse
Series Title: Lecture Notes in Mathematics
DOI: https://doi.org/10.1007/978-3-319-02231-4
Publisher: Springer Cham
eBook Packages: Mathematics and Statistics, Mathematics and Statistics (R0)
Copyright Information: Springer International Publishing Switzerland 2014
Softcover ISBN: 978-3-319-02230-7Published: 25 November 2013
eBook ISBN: 978-3-319-02231-4Published: 18 November 2013
Series ISSN: 0075-8434
Series E-ISSN: 1617-9692
Edition Number: 1
Number of Pages: XIV, 177
Number of Illustrations: 4 b/w illustrations
Topics: Numerical Analysis, Probability Theory and Stochastic Processes, Partial Differential Equations