A stabilized hybrid discontinuous Galerkin method for the Cahn–Hilliard equation

Abstract

In this paper, we present a stabilized mixed hybrid discontinuous Galerkin finite element method for solving fourth-order parabolic problems such as the Cahn–Hilliard equation used to describe the dynamics of avascular tumor growth. The proposed method is compared to other methods previously studied in this context. Several numerical experiments are presented to show convergence, performance and accuracy comparisons with other methods. Besides, we also show the ability of the method to solve a complex case of avascular tumor growth where the behavior of tumor cells towards nutrient gradients drives fingering instabilities. The results show the great potential of the presented method for the efficient and accurate solution of Cahn–Hilliard problems which includes applications on complex tumor growth problems.