SEMIDISCRETE FINITE ELEMENT APPROXIMATION OF STOCHASTIC NONSELFADJOINT WAVE EQUATION
Li Xiaocui1, Yang Xiaoyuan1, Zhang Yinghan2
1. Department of Mathematics, Beihang University, LMIB of the Ministry of Education, Beijing 100191, China;
2. School of Mathematics and Physics, University of Science and Technology Beijing, Beijing 100083, China
We study the semidiscrete finite element approximation of the linear stochastic nonselfadjoint 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 discretisation and the properties of a strongly continuous operator cosine function are used.The error estimates are applicable in the multi-dimensional case.
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