Finite element approximation of the linear stochastic wave equation with additive noise
Journal article, 2010
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.
strong convergence
a priori error estimate
inite element method
stochastic wave equation
stability
Wiener process
additive noise
Author
Mihaly Kovacs
Chalmers, Mathematical Sciences, Mathematics
University of Gothenburg
Stig Larsson
Chalmers, Mathematical Sciences, Mathematics
University of Gothenburg
Fardin Saedpanah
Chalmers, Mathematical Sciences, Mathematics
University of Gothenburg
SIAM Journal on Numerical Analysis
0036-1429 (ISSN) 1095-7170 (eISSN)
Vol. 48 2 408-427Subject Categories
Computational Mathematics
DOI
10.1137/090772241