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BIT Numerical Mathematics

, Volume 44, Issue 4, pp 829–847 | Cite as

Semidiscrete Galerkin Approximation for a Linear Stochastic Parabolic Partial Differential Equation Driven by an Additive Noise

  • Yubin Yan
Article

Abstract

We study the semidiscrete Galerkin approximation of a stochastic parabolic partial differential equation forced by an additive space-time noise. The discretization in space is done by a piecewise linear finite element method. The space-time noise is approximated by using the generalized L2 projection operator. Optimal strong convergence error estimates in the L2 and \(\dot{H}^{-1}\) norms with respect to the spatial variable are obtained. The proof is based on appropriate nonsmooth data error estimates for the corresponding deterministic parabolic problem. The error estimates are applicable in the multi-dimensional case.

Keywords

stochastic parabolic partial differential equations finite element method additive noise Hilbert space 

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Copyright information

© Kluwer Academic Publishers 2004

Authors and Affiliations

  1. 1.Department of MathematicsThe University of ManchesterManchesterEngland

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