Journal of Computational Physics
Systems of Cahn-Hilliard equations
SIAM Journal on Applied Mathematics
Journal of Computational Physics
The Runge-Kutta discontinuous Galerkin method for conservation laws V multidimensional systems
Journal of Computational Physics
The Local Discontinuous Galerkin Method for Time-Dependent Convection-Diffusion Systems
SIAM Journal on Numerical Analysis
Finite Element Approximation of the Cahn--Hilliard Equation with Degenerate Mobility
SIAM Journal on Numerical Analysis
Multigrid
A Local Discontinuous Galerkin Method for KdV Type Equations
SIAM Journal on Numerical Analysis
Journal of Scientific Computing
Conservative multigrid methods for Cahn-Hilliard fluids
Journal of Computational Physics
A multigrid finite element solver for the Cahn-Hilliard equation
Journal of Computational Physics
Local discontinuous Galerkin methods for the Cahn-Hilliard type equations
Journal of Computational Physics
Journal of Scientific Computing
Efficient Solvers of Discontinuous Galerkin Discretization for the Cahn---Hilliard Equations
Journal of Scientific Computing
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In this paper, we develop an efficient and energy stable fully-discrete local discontinuous Galerkin (LDG) method for the Cahn-Hilliard-Hele-Shaw (CHHS) system. The semi-discrete energy stability of the LDG method is proved firstly. Due to the strict time step restriction (@Dt=O(@Dx^4)) of explicit time discretization methods for stability, we introduce a semi-implicit time integration scheme which is based on a convex splitting of the discrete Cahn-Hilliard energy. The unconditional energy stability has been proved for this fully-discrete LDG scheme. The fully-discrete equations at the implicit time level are nonlinear. Thus, the nonlinear Full Approximation Scheme (FAS) multigrid method has been applied to solve this system of algebraic equations, which has been shown the nearly optimal complexity numerically. Numerical results are also given to illustrate the accuracy and capability of the LDG method coupled with the multigrid solver.