An Unconditionally Energy-Stable SAV-DG Numerical Scheme for Tumor Growth Model

Abstract

In this paper, we propose a linear, fully decoupled and unconditionally energy-stable discontinuous Galerkin (DG) method for solving the tumor growth model, which is derived from the variation of the free energy. The fully discrete scheme is constructed by the scalar auxiliary variable (SAV) for handling the nonlinear term and backward Euler method for the time discretization. We rigorously prove the unconditional energy stability and optimal error estimates of the scheme. Finally, several numerical experiments are performed to verify the energy stability and validity of the proposed scheme.