High Order Energy Stable and Efficient Local Discontinuous Galerkin Methods for the Phase Field Models
University of Science and Technology of China
2017-06-12 ~ 2017-06-12
Science Building No. 1 1493
The goal of this talk is to propose two energy stable fully discrete local discontinuous Galerkin(LDG) finite element methods for the phase field models. Based on the method of lines, we first construct an LDG method and prove the semi-discrete energy stability. Then, we develop a first order and a second order semi-implicit convex splitting schemes based on a convex splitting principle of the discrete Cahn-Hilliard energy, and prove the corresponding unconditional energy stabilities. In addition, a semi-implicit spectral deferred correction（SDC）method combining the first order convex splitting scheme is employed to improve the temporal accuracy. The SDC method is high order accurate and stable numerically with the time step proportional to the spatial mesh size. The resulting algerbraic equations at the implicit level are nonlinear. Due to the local properties of the LDS methods, the resulting implicit scheme is easy to implement and can be solved in an explicit way when it is coupled with iterative methods. An efficient nonlinear multigrid method is used to solve the equations. Numerical experiments of the accuracy and long time simulations are presented to illustrate the high order accuracy in both time and space, the capability and efficiency of the proposed methods.