A stochastic finite element method for stochastic parabolic equations driven by purely spatial noise
Chia Ying Lee, Boris L. Rozovskii · Communications on Stochastic Analysis · 2010
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 element method applied to a class of equations with self-adjoint differential 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).