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

作者：Aboelenen Tarek^*; El Hawary H M

来源：Computers & Mathematics with Applications, 2017, 73(6): 1197-1217.

DOI：10.1016/j.camwa.2016.07.018

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

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.

• 出版日期2017-3-15