NDLI: On the Convergence Analysis of the Inexact Linearly Implicit Euler Scheme for a Class of Stochastic Partial Differential Equations

Content Provider	Springer Nature Link
Author	Schilling, R. L. Döhring, N. Raasch, T. Friedrich, U. Lindner, F. Ritter, K. Cioica, P. A. Dahlke, S. Kinzel, S.
Copyright Year	2015
Abstract	This paper is concerned with the adaptive numerical treatment of stochastic partial differential equations. Our method of choice is Rothe’s method. We use the implicit Euler scheme for the time discretization. Consequently, in each step, an elliptic equation with random right-hand side has to be solved. In practice, this cannot be performed exactly, so that efficient numerical methods are needed. Well-established adaptive wavelet or finite-element schemes, which are guaranteed to converge with optimal order, suggest themselves. We investigate how the errors corresponding to the adaptive spatial discretization propagate in time, and we show how in each time step the tolerances have to be chosen such that the resulting perturbed discretization scheme realizes the same order of convergence as the one with exact evaluations of the elliptic subproblems.
Ending Page	495
Page Count	23
Starting Page	473
File Format	PDF
ISSN	09262601
e-ISSN	1572929X
Journal	Potential Analysis
Issue Number	3
Volume Number	44
Language	English
Publisher	Springer Netherlands
Publisher Date	2016-01-07
Publisher Place	Dordrecht
Access Restriction	One Nation One Subscription (ONOS)
Subject Keyword	Stochastic partial differential equations Probability Theory and Stochastic Processes Stochastic partial differential equation Euler scheme Rothe’s method Convergence analysis Geometry Stochastic evolution equation Solution of discretized equations Potential Theory Functional Analysis Computational methods for stochastic equations Adaptive numerical algorithm
Content Type	Text
Resource Type	Article
Subject	Analysis

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