No abstract

No abstract

In this paper, we propose a local discontinuous Galerkin (LDG) method for fully nonlinear and possibly degenerate parabolic stochastic partial differential equations (SPDEs), which is a high-order numerical scheme. This method is an extension of the discontinuous Galerkin (DG) method for purely hyperbolic equations to parabolic equations and share with the DG method its advantage and flexibility. We prove the $L^2$-stability of the numerical scheme for fully nonlinear equations. Optimal error estimates ($\cO(h^{k+1})$) for smooth solutions of semilinear stochastic equations is shown if polynomials of degree $k$ are used. We also develop an explicit derivative-free order $1.5$ time discretization scheme to solve the matrix-valued stochastic ordinary differential equations derived from the spatial discretization. Numerical examples displaying the performance of the method are shown.

No abstract

No abstract