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We consider parabolic SPDEs driven by purely spatial noise, and show the existence of solutions with random initial data and forcing terms. We perform error analysis for the semi-discrete stochastic finite el- ement method applied to a class of equations with self-adjoint dierential operators that are independent of time. The analysis employs the formal stochastic adjoint problem and the corresponding elliptic error estimates to obtain the optimal order of convergence (in space).

A stochastic finite element method for stochastic parabolic equations driven by purely spatial noise