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Title: 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 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 L 2 -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.  more » « less
Award ID(s):
1719410
PAR ID:
10226111
Author(s) / Creator(s):
; ;
Date Published:
Journal Name:
ESAIM: Mathematical Modelling and Numerical Analysis
Volume:
55
Issue:
Supplement
ISSN:
0764-583X
Page Range / eLocation ID:
S187 to S223
Format(s):
Medium: X
Sponsoring Org:
National Science Foundation
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