A high-order nodal discontinuous Galerkin method for a linearized fractional Cahn–Hilliard equation

Tarek Aboelenen, H. M. El-Hawary

Research output: Contribution to journalJournal articlepeer-review

13 Scopus citations

Abstract

In this paper, we develop and analyze a nodal discontinuous Galerkin method for the linearized fractional Cahn–Hilliard equation containing derivatives of fractional order in space. The Caputo derivative is chosen as the representation of spatial derivative. The linearized fractional Cahn–Hilliard problem has been expressed as a system of low order differential/integral equations. We adopt the nodal discontinuous Galerkin methods for the full spatial discretization using a high-order nodal basis set of orthonormal Lagrange–Legendre polynomials of arbitrary order in space on each element of computational domain. Moreover, we prove the stability and optimal order of convergence N+1 for the linearized fractional Cahn–Hilliard problem when polynomials of degree N are used. Numerical experiments are displayed to verify the theoretical results.

Original languageEnglish
Pages (from-to)1197-1217
Number of pages21
JournalComputers and Mathematics with Applications
Volume73
Issue number6
DOIs
StatePublished - 15 Mar 2017
Externally publishedYes

Keywords

  • Error estimates
  • Linearized fractional Cahn–Hilliard equation
  • Nodal discontinuous Galerkin method
  • Stability

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