Volume 55, 2021Regular articles published in advance of the transition of the journal to Subscribe to Open (S2O). Free supplement sponsored by the Fonds National pour la Science Ouverte
|Page(s)||S187 - S223|
|Published online||26 February 2021|
A local discontinuous Galerkin method for nonlinear parabolic SPDEs
Department of Finance and Control Sciences, School of Mathematical Sciences, Fudan University, Shanghai 200433, P.R. China
2 Division of Applied Mathematics, Brown University, Providence, RI 02912, USA
* Corresponding author: Chi-Wang_Shu@brown.edu
Accepted: 13 April 2020
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 the L2-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 degree k are 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.
Mathematics Subject Classification: 65C30 / 60H35
Key words: Local discontinuous Galerkin method / nonlinear parabolic stochastic partial differential equations / multiplicative noise / stability analysis / error estimates / stochastic viscous Burgers equation
© EDP Sciences, SMAI 2021
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