Premium
Numerical error analysis for nonsymmetric interior penalty discontinuous Galerkin method of Cahn–Hilliard equation
Author(s) -
Liu Chen,
Frank Florian,
Rivière Béatrice M.
Publication year - 2019
Publication title -
numerical methods for partial differential equations
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.901
H-Index - 61
eISSN - 1098-2426
pISSN - 0749-159X
DOI - 10.1002/num.22362
Subject(s) - mathematics , cahn–hilliard equation , discontinuous galerkin method , galerkin method , a priori and a posteriori , convergence (economics) , stability (learning theory) , penalty method , error analysis , mathematical analysis , finite element method , mathematical optimization , partial differential equation , computer science , philosophy , physics , epistemology , machine learning , economics , thermodynamics , economic growth
In this paper, we derive a theoretical analysis of nonsymmetric interior penalty discontinuous Galerkin methods for solving the Cahn–Hilliard equation. We prove unconditional unique solvability of the discrete system and derive stability bounds with a generalized chemical energy density. Convergence of the method is obtained by optimal a priori error estimates. Our analysis is valid for both symmetric and nonsymmetric versions of the discontinuous Galerkin formulation.