Journal
JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS
Volume 402, Issue -, Pages -Publisher
ELSEVIER
DOI: 10.1016/j.cam.2021.113800
Keywords
Discontinuous Galerkin; Hybridization; Allen-Cahn equation; Error analysis; Energy stable
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This paper presents an energy-stable hybridizable interior penalty discontinuous Galerkin method for the Allen-Cahn equation, proving its energy stability, existence, and uniqueness. The method's effectiveness and convergence are numerically verified through several examples.
This paper presents an energy-stable hybridizable interior penalty discontinuous Galerkin method for the Allen-Cahn equation. To obtain an unconditionally energy stable scheme, the energy potential is split into a sum of a convex and concave function. Energy stability for the proposed scheme is proven to hold for arbitrary time. Existence and uniqueness for the scheme is also established. Under standard assumptions on the energy potential (Lipschitz continuity), we demonstrate rigorously that the method converges optimally for symmetric schemes, and suboptimally for nonsymmetric schemes. Several examples are provided which numerically verify and validate the method. (C) 2021 Published by Elsevier B.V.
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