| Issue |
ESAIM: M2AN
Volume 55, 2021
Regular 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 | |
| DOI | https://doi.org/10.1051/m2an/2020026 | |
| Published online | 26 February 2021 | |
A local discontinuous Galerkin method for nonlinear parabolic SPDEs
1
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
Received:
18
May
2019
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
Current usage metrics show cumulative count of Article Views (full-text article views including HTML views, PDF and ePub downloads, according to the available data) and Abstracts Views on Vision4Press platform.
Data correspond to usage on the plateform after 2015. The current usage metrics is available 48-96 hours after online publication and is updated daily on week days.
Initial download of the metrics may take a while.