Error Estimate on Crank-Nicolson Scheme for Stochastic Parabolic Partial Differential Equations
In this paper we study a numerical method for the partial equations. Firstly, we introduce the basic conceptions and properties of the space, operator, stochastic partial equations and! the finite element method. Then we mainly describe and analyze the finite element method for a stochastic parabolic partial problem with homogeneous Dirichlet boundary conditions. The discretization with respect to space is done by piecewise linear finite elements, and in time we apply the C-N method. Optimal convergence error estimates in the L(2) and H(-1) norms are obtained, and the rigorous prove is given.
partial equations operator space the finite element normal