FINITE ELEMENT APPROXIMATION OF THE LINEAR STOCHASTIC WAVE EQUATION WITH ADDITIVE NOISE

被引：56

作者：

Kovacs, Mihaly ^{[1
]}

Larsson, Stig ^{[2
,3
]}

Saedpanah, Fardin ^{[2
,3
]}

机构：

[1] Univ Otago, Dept Math & Stat, Dunedin, New Zealand

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

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

来源：

SIAM JOURNAL ON NUMERICAL ANALYSIS | 2010年 / 48卷 / 02期

基金：

瑞典研究理事会;

关键词：

finite element method; stochastic wave equation; additive noise; Wiener process; stability; a priori error estimate; strong convergence; PARTIAL-DIFFERENTIAL-EQUATIONS; ORDER HYPERBOLIC EQUATIONS; CONVERGENCE; DRIVEN;

D O I：

10.1137/090772241

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

Semidiscrete finite element approximation of the linear stochastic wave equation (LSWE) with additive noise is studied in a semigroup framework. Optimal error estimates for the deterministic problem are obtained under minimal regularity assumptions. These are used to prove strong convergence estimates for the stochastic problem. The theory presented here applies to multidimensional domains and spatially correlated noise. Numerical examples illustrate the theory.

引用

页码：408 / 427

页数：20

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