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.
Article PDF
We’re sorry, something doesn't seem to be working properly.
Please try refreshing the page. If that doesn't work, please contact support so we can address the problem.
Avoid common mistakes on your manuscript.
Author information
Authors and Affiliations
Corresponding author
Additional information
AMS subject classification (2000)
65M, 60H15, 65C30, 65M65.
Received April 2004. Revised September 2004. Communicated by Anders Szepessy.
Rights and permissions
About this article
Cite this article
Yan, Y. Semidiscrete Galerkin Approximation for a Linear Stochastic Parabolic Partial Differential Equation Driven by an Additive Noise. Bit Numer Math 44, 829–847 (2004). https://doi.org/10.1007/s10543-004-3755-5
Issue Date:
DOI: https://doi.org/10.1007/s10543-004-3755-5