A BOUND OF DISCONTINUOUS GALERKIN SOLUTIONS FOR THE CHAN-HILLIARD EQUATION

Abstract

Cahn-Hilliard equation is modeled to describe the phase separation in systems. Using a discontinuous Galerkin method, we will control accuracy of approximate solutions. In this paper, boundedness of discontinuous Galerkin solution is discussed. A posteriori error estimation of the Cahn-Hilliard equation, which is based on the results of this paper, will be studied later.

Cahn-Hilliard equation is modeled to describe the phase separation in systems. Using a discontinuous Galerkin method, we will control accuracy of approximate solutions. In this paper, boundedness of discontinuous Galerkin solution is discussed. A posteriori error estimation of the Cahn-Hilliard equation, which is based on the results of this paper, will be studied later.