Numerical Approximation to A Stochastic Parabolic PDE with Weak Galerkin Method

摘要

The weak Galerkin finite element method is a class of recently and rapidly developed numerical tools for approximating partial differential equations.Unlike the standard Galerkin method,its trial and test function spaces consist of totally discontinuous piecewisely defined polynomials in the whole domain.This method has been vastly applied to many fields [22,28,31,44,50-52].In this paper,we will apply this method to approximate a stochastic parabolic partial differential equation.We set up a semi-discrete numerical scheme for the stochastic partial differential equations and derive the optimal order for error estimates in the sense of strong convergence.