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

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.