Adaptive finite element method for wick stochastic partial differential equations

Abstract

In this paper we approximate the solution of the wick stochastic partial differential equation by the affine conforming finite element method. Then we provide a priori and a posteriori error estimations and prove the convergence of the numerical method. In particular, we construct a Galerkin approximation scheme and we derive the local residual based on posteriori error indicator, all the while proving its efficiency and reliability. Finally, two numerical examples are presented and analysed to illustrate the derived theoretical results, the effectiveness of the proposed adaptive algorithm and the good behaviour of the numerical solution and the mesh adaptation strategy used.