Numerical solutions to time-fractional stochastic partial differential equations
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This study is concerned with numerical approximations of time-fractional stochastic heat-type equations driven by multiplicative noise, which can be used to model the anomalous diffusion in porous media with random effects with thermal memory. A standard finite element approximation is used in space as well as a spatial-temporal discretization which is achieved by a new algorithm in time direction. The strong convergence error estimates for both semidiscrete and fully discrete schemes in a semigroup framework are proved, which are based on the error estimates for the corresponding deterministic equations, and together with the optimal regularity results of mild solutions to the time-fractional SPDEs. Numerical results are finally reported to confirm our theoretical findings.
KeywordsTime-fractional derivative Stochastic heat-type equations Finite element method Error estimates
Mathematics Subject Classification (2010)65C30 65N30
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We thank the referees very much for the constructive comments and valuable suggestions which would help us to improve the quality of the paper.
This study is supported by the National Nature Science Foundation of China (Grant No. 11626085) and Key Scientifc Research Projects of Colleges and Universities in Henan Province, China (19A110002).