A local discontinuous Galerkin method for nonlinear parabolic SPDEs
Abstract
In this paper, we propose a local discontinuous Galerkin (LDG) method for nonlinear and possibly degenerate parabolic stochastic partial differential equations, which is a high-order numerical scheme. It extends the discontinuous Galerkin (DG) method for purely hyperbolic equations to parabolic equations and shares with the DG method its advantage and flexibility. We prove theL2-stability of the numerical scheme for fully nonlinear equations. Optimal error estimates (O(h(k+1))) for smooth solutions of semi-linear stochastic equations is shown if polynomials of degreekare used. We use 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 are given to display the performance of the LDG method.
Document Details
- Document Type
- Pub Defense Publication
- Publication Date
- Jan 01, 2021
- Source ID
- 10.1051/m2an/2020026
Entities
People
- Chi-Wang Shu
- Shanjian Tang
- Yunzhang Li
Organizations
- Army Research Office
- National Natural Science Foundation of China
- National Science Foundation