Numerical schemes for a three component Cahn-Hilliard model
نویسندگان
چکیده
In this article, we investigate numerical schemes for solving a three component CahnHilliard model. The space discretization is performed by using a Galerkin formulation and the finite element method. Concerning the time discretization, the main difficulty is to write a scheme ensuring, at the discrete level, the decrease of the free energy and thus the stability of the method. We study three different schemes and prove existence and convergence theorems. Theoretical results are illustrated by various numerical examples showing that the new semi-implicit discretization that we propose seems to be a good compromise between robustness and accuracy. 1991 Mathematics Subject Classification. 35K55, 65M60, 65M12, 76T30.
منابع مشابه
Numerical Approximations for a Three Components Cahn-hilliard Phase-field Model Based on the Invariant Energy Quadratization Method
How to develop efficient numerical schemes while preserving the energy stability at the discrete level is a challenging issue for the three component Cahn-Hilliard phase-field model. In this paper, we develop first and second order temporal approximation schemes based on the “Invariant Energy Quadratization” approach, where all nonlinear terms are treated semi-explicitly. Consequently, the resu...
متن کاملNumerical Approximations for a Three Component Cahn-hilliard Phase-field Model Based on the Invariant Energy Quadratization Method
How to develop efficient numerical schemes while preserving the energy stability at the discrete level is a challenging issue for the three component Cahn-Hillard phase-field model. We develop in this paper first and second order temporal approximation schemes based on the “Invariant Energy Quadratization” method, where all nonlinear terms are treated semi-explicitly. Consequently, the resultin...
متن کاملFully Discrete Approximation of a Three Component Cahn-hilliard Model
In this paper, we investigate numerical schemes for solving a three component CahnHilliard model. The space discretization is performed by using a Galerkin formulation and the finite element method. For the time discretization, the main difficulty is to write a scheme ensuring, at the discrete level, the decrease of the energy. We study three different schemes and propose existence and converge...
متن کاملEnergy Stable Schemes for Cahn-Hilliard Phase-Field Model of Two-Phase Incompressible Flows∗∗∗
Numerical approximations of Cahn-Hilliard phase-field model for the two-phase incompressible flows are considered in this paper. Several efficient and energy stable time discretization schemes for the coupled nonlinear Cahn-Hilliard phase-field system for both the matched density case and the variable density case are constructed, and are shown to satisfy discrete energy laws which are analogou...
متن کاملEfficient Energy Stable Schemes with Spectral Discretization in Space for Anisotropic Cahn–hilliard Systems
We develop in this paper efficient and robust numerical methods for solving anisotropic Cahn–Hilliard systems. We construct energy stable schemes for the time discretization of the highly nonlinear anisotropic Cahn-Hilliard systems by using a stabilization technique. At each time step, these schemes lead to a sequence of linear coupled elliptic equations with constant coefficients which can be ...
متن کامل