A local discontinuous Galerkin method for nonlinear parabolic SPDEs

In this paper, we propose a local discontinuous Galerkin (LDG) method for nonlinear and possibly degenerate parabolic stochastic partial differential equations, which is high-order numerical scheme. It extends the (DG) purely hyperbolic equations to shares with DG its advantage flexibility. We prove L 2 -stability of scheme fully equations. Optimal error estimates ( O h (k+1) )) smooth solutions semi-linear shown if polynomials degree k are used. use an explicit derivative-free order 1.5 time discretization solve matrix-valued ordinary derived from spatial discretization. Numerical examples given display performance LDG method.