An efficient, unconditionally energy stable local discontinuous Galerkin scheme for the Cahn-Hilliard-Brinkman system

Ruihan Guo

Ancienne Post-doctorante MILYON – Université Claude Bernard Lyon 1 – ICJ

→ du 01/09/2014 au 31/08/2016

Abstract: We present an efficient and unconditionally energy stable fully-discrete local discontinuous Galerkin (LDG) method for approximating the Cahn-Hilliard-Brinkman (CHB) system. The semi-discrete energy stability of the LDG method is proved firstly.

Due to the strict time step restriction (Δt = Ox4)) of explicit time discretization methods for stability, we introduce a semi-implicit scheme for the temporal discretization.

The unconditional energy stability for this fully-discrete LDG scheme is also proved. 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, and the nearly optimal complexity has been shown numerically.

Keywords: Cahn-Hilliard-Brinkman system, local discontinuous Galerkin method, energy stability, convex splitting, multigrid

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