ANALYSIS OF SOME SPLITTING SCHEMES FOR THE STOCHASTIC ALLEN-CAHN EQUATION

被引：38

作者：

Brehier, Charles-Edouard ^{[1
]}

Goudenege, Ludovic ^{[2
]}

机构：

[1] Univ Lyon, CNRS, Univ Claude Bernard Lyon 1, UMR5208,Inst Camille Jordan, 43 Blvd 11 Novembre 1918, F-69622 Villeurbanne, France

[2] Univ Paris Saclay, CNRS,FR3487, Federat Mathemat CentraleSupelec, CentraleSupelec, 3 Rue Joliot Curie, F-91190 Gif Sur Yvette, France

来源：

DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS-SERIES B | 2019年 / 24卷 / 08期

关键词：

Stochastic partial differential equations; splitting schemes; Allen-Cahn equation; PARTIAL-DIFFERENTIAL-EQUATIONS; FINITE-ELEMENT DISCRETIZATION; STRONG-CONVERGENCE; NUMERICAL APPROXIMATIONS; LATTICE APPROXIMATIONS; IMPLICIT SCHEME; LEVEL SETS; UP METHOD; TIME; SPDES;

D O I：

10.3934/dcdsb.2019077

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We introduce and analyze an explicit time discretization scheme for the one-dimensional stochastic Allen-Cahn, driven by space-time white noise. The scheme is based on a splitting strategy, and uses the exact solution for the nonlinear term contribution. We first prove boundedness of moments of the numerical solution. We then prove strong convergence results: first, L-2(Omega)-convergence of order almost 1/4, localized on an event of arbitrarily large probability, then convergence in probability of order almost 1/4. The theoretical analysis is supported by numerical experiments, concerning strong and weak orders of convergence.

引用

页码：4169 / 4190

页数：22

共 62 条

[1] MICROSCOPIC THEORY FOR ANTIPHASE BOUNDARY MOTION AND ITS APPLICATION TO ANTIPHASE DOMAIN COARSENING [J].