FULL DISCRETIZATION OF SEMILINEAR STOCHASTIC WAVE EQUATIONS DRIVEN BY MULTIPLICATIVE NOISE

被引：59

作者：

Anton, Rikard ^{[1
]}

Cohen, David ^{[1
,2
]}

Larsson, Stig ^{[3
,4
]}

Wang, Xiaojie ^{[5
]}

机构：

[1] Umea Univ, Dept Math & Math Stat, SE-90187 Umea, Sweden

[2] Univ Innsbruck, Dept Math, A-6020 Innsbruck, Austria

[3] Chalmers, Dept Math Sci, SE-41296 Gothenburg, Sweden

[4] Univ Gothenburg, SE-41296 Gothenburg, Sweden

[5] Cent S Univ, Sch Math & Stat, CN-410083 Changsha, Hunan, Peoples R China

来源：

SIAM JOURNAL ON NUMERICAL ANALYSIS | 2016年 / 54卷 / 02期

基金：

瑞典研究理事会;

关键词：

semilinear stochastic wave equation; multiplicative noise; strong convergence; trace formula; stochastic trigonometric methods; geometric numerical integration; PARTIAL-DIFFERENTIAL-EQUATIONS; FINITE-ELEMENT METHODS; ADDITIVE NOISE; APPROXIMATION;

D O I：

10.1137/15M101049X

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

A fully discrete approximation of the semilinear stochastic wave equation driven by multiplicative noise is presented. A standard linear finite element approximation is used in space, and a stochastic trigonometric method is used for the temporal approximation. This explicit time integrator allows for mean-square error bounds independent of the space discretization and thus does not suffer from a step size restriction as in the often used Stormer-Verlet leapfrog scheme. Furthermore, it satisfies an almost trace formula (i.e., a linear drift of the expected value of the energy of the problem). Numerical experiments are presented and confirm the theoretical results.

引用

页码：1093 / 1119

页数：27

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