×

Semidiscrete finite element approximation of stochastic non-selfadjoint wave equation. (Chinese. English summary) Zbl 1399.65258

Summary: We study the semidiscrete finite element approximation of the linear stochastic non-selfadjoint wave equation forced by additive noise. The results here are more general since the linear operator \(A\) does not need to be self-adjoint and we do not need information about eigenvalues and eigenfunctions of the linear operator \(A\). In order to obtain the strong convergence error estimates, a standard finite element method for the spatial discretization and the properties of a strongly continuous operator cosine function are used. The error estimates are applicable in the multi-dimensional case.

MSC:

65M60 Finite element, Rayleigh-Ritz and Galerkin methods for initial value and initial-boundary value problems involving PDEs
65C30 Numerical solutions to stochastic differential and integral equations
65M15 Error bounds for initial value and initial-boundary value problems involving PDEs
65M12 Stability and convergence of numerical methods for initial value and initial-boundary value problems involving PDEs
35R60 PDEs with randomness, stochastic partial differential equations
PDFBibTeX XMLCite