High order unconditionally energy stable RKDG schemes for the Swift–Hohenberg equation

We propose unconditionally energy stable Runge–Kutta (RK) discontinuous Galerkin (DG) schemes for solving a class of fourth order gradient flows including the Swift–Hohenberg equation. Our algorithm is geared toward arbitrarily high order approximations in both space and time, while energy dissipati...

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Bibliographic Details
Published in:Journal of computational and applied mathematics 2022-06, Vol.407 (C), p.114015, Article 114015
Main Authors: Liu, Hailiang, Yin, Peimeng
Format: Article
Language:English
Subjects:
DG methods
Energy stability
EQ approach
Gradient flows
RK method
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Summary:We propose unconditionally energy stable Runge–Kutta (RK) discontinuous Galerkin (DG) schemes for solving a class of fourth order gradient flows including the Swift–Hohenberg equation. Our algorithm is geared toward arbitrarily high order approximations in both space and time, while energy dissipation remains preserved for arbitrary time steps and spatial meshes. The method integrates a penalty free DG method for spatial discretization with a multi-stage algebraically stable RK method for temporal discretization by the energy quadratiztion (EQ) strategy. The resulting fully discrete DG method is proven to be unconditionally energy stable. By numerical tests on several benchmark problems we demonstrate the high order accuracy, energy stability, and simplicity of the proposed algorithm.
ISSN:0377-0427
1879-1778
DOI:10.1016/j.cam.2021.114015