Unconditionally energy stable discontinuous Galerkin schemes for the Cahn-Hilliard equation
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In this paper, we introduce novel discontinuous Galerkin (DG) schemes for the Cahn-Hilliard equation to produce free-energy-dissipating and mass conservative discrete solutions, irrespective of the time step and the mesh size. We integrate the mixed DG method for the spatial discretization with the Energy Quadratization (EQ) approach for the time discretization. Coupled with a spatial projection, the resulting EQ-DG schemes can be efficiently solved without resorting to any iterative method. The schemes are shown to be unconditionally energy dissipative and mass conservative. Both one and two dimensional numerical examples verify our theoretical results, and demonstrate the good performance of EQ-DG on efficiency, accuracy, and preservation of the desired solution properties.
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