Optimal Strong Rates of Convergence for a Space-Time Discretization of the Stochastic Allen–Cahn Equation with Multiplicative Noise

The stochastic Allen–Cahn equation with multiplicative noise involves the nonlinear drift operator . We use the fact that satisfies a weak monotonicity property to deduce uniform bounds in strong norms for solutions of the temporal, as well as of the spatio-temporal discretization of the problem. Th...

Full description

Saved in:
Bibliographic Details
Published inJournal of computational methods in applied mathematics Vol. 18; no. 2; pp. 297 - 311
Main Authors Majee, Ananta K., Prohl, Andreas
Format Journal Article
LanguageEnglish
Published Minsk De Gruyter 01.04.2018
Walter de Gruyter GmbH
Subjects
45K05
46S50
49L20
49L25
91A23
93E20
Discretization
Monotone Operator
Norms
Spacetime
Stochastic Allen–Cahn Equation
Strong Rate ofConvergence
Variational Solution
Online AccessGet full text
ISSN1609-4840
1609-9389
DOI10.1515/cmam-2017-0023

Cover

More Information
Summary:The stochastic Allen–Cahn equation with multiplicative noise involves the nonlinear drift operator . We use the fact that satisfies a weak monotonicity property to deduce uniform bounds in strong norms for solutions of the temporal, as well as of the spatio-temporal discretization of the problem. This weak monotonicity property then allows for the estimate for all small , where is the strong variational solution of the stochastic Allen–Cahn equation, while solves a structure preserving finite element based space-time discretization of the problem on a temporal mesh of size which covers
Bibliography:ObjectType-Article-1
SourceType-Scholarly Journals-1
ObjectType-Feature-2
content type line 14
ISSN:1609-4840
1609-9389
DOI:10.1515/cmam-2017-0023