A quadratic reformulation of rational-like energies yields an auxiliary-variable discretization of the Cahn-Hilliard equation that inherits the original energy decay property.
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High-order essentially explicit discretizations using Fourier Galerkin plus projection-relaxation conserve mass, momentum, and energy for BBM, KdV, and NLS equations.
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Energy stable auxiliary variable method for Cahn--Hilliard equations
A quadratic reformulation of rational-like energies yields an auxiliary-variable discretization of the Cahn-Hilliard equation that inherits the original energy decay property.
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Conserving mass, momentum, and energy for the Benjamin-Bona-Mahony, Korteweg-de Vries, and nonlinear Schr\"odinger equations
High-order essentially explicit discretizations using Fourier Galerkin plus projection-relaxation conserve mass, momentum, and energy for BBM, KdV, and NLS equations.