Strong convergence of an fractional exponential integrator scheme for the finite element discretization of time-fractional SPDE driven by standard and fractional Brownian motions

作     者：Noupelah, Aurelien Junior Tambue, Antoine Woukeng, Jean Louis 

作者机构：Department of Mathematics and Computer Sciences University of Dschang P.O. BOX 67 Dschang Cameroon Department of Computer Science Electrical Engineering and Mathematical Sciences Western Norway University of Applied Sciences Inndalsveien 28 Bergen5063 Norway 

出 版 物：《arXiv》 (arXiv)

年 卷 期：2022年

核心收录：

主　　题：Stochastic systems 

摘      要：The aim of this work is to provide the first strong convergence result of numerical approximation of a general time-fractional second order stochastic partial differential equation involving a Caputo derivative in time of order α ϵ (1/2;1) and driven simultaneously by a multiplicative standard Brownian motion and additive fBm with Hurst parameter H ϵ (1.2, 1), more realistic to model the random effects on transport of particles in medium with thermal memory. We prove the existence and uniqueness results and perform the spatial discretization using the finite element and the temporal discretization using a fractional exponential integrator scheme. We provide the temporal and spatial convergence proofs for our fully discrete scheme and the result shows that the convergence orders depend on the regularity of the initial data, the power of the fractional derivative, and the Hurst parameter H. Copyright © 2022, The Authors. All rights reserved.