ON the SUPERCONVERGENCE of a HYBRIDIZABLE DISCONTINUOUS GALERKIN METHOD for the CAHN-HILLIARD EQUATION

Abstract

We Propose a Hybridizable Discontinuous Galerkin (HDG) Method with the Convex-Concave Splitting Temporal Discretization for Solving the Cahn-Hilliard Equation. We Establish Optimal Convergence Rates for the Scalar Variables and the Flux Variables in the L2 Norm for Polynomials of Degree K ≥ 0. the Error Constants Depend on Inverse of the Interface Thickness in Polynomial Orders, Which is Obtained by Utilizing a Spectral-Type Estimate of the Discrete Cahn-Hilliard Operator in the HDG Framework. in Terms of Degrees of Freedom of the Globally Coupled Unknowns, the Scalar Variables Are Superconvergent. Numerical Results Are Reported to Corroborate the Theoretical Convergence Rates and the Effectiveness of the Method.

Department(s)

Mathematics and Statistics

Comments

National Science Foundation, Grant DMS-1818867

Keywords and Phrases

Cahn-Hilliard; finite element; HDG method; superconvergence

International Standard Serial Number (ISSN)

0036-1429

Document Type

Article - Journal

Document Version

Final Version

File Type

text

Language(s)

English

Rights

© 2023 Society for Industrial and Applied Mathematics, All rights reserved.

Publication Date

01 Jan 2023

Link to Full Text

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