Randomized trial investigates strong convergence in finite element approximation of wave equations with noise, indicating improved predictions.
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.
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Kovács et al. (2010) studied this question.
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