New energetic spectral-element time integrators for phase-field gradient systems that preserve discrete energy dissipation and mass conservation, with numerical tests showing better performance than BDF4 and ETDRK4 on Allen-Cahn problems.
Efficient high order semi-implicit time discretization and local discontinuous Galerkin methods for highly nonlinear PDEs
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Develops energy-stable asymptotic-preserving discretizations of a hyperbolized Cahn-Hilliard equation via SBP operators and IMEX Runge-Kutta methods guided by relative-energy error estimates.
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Energetic Spectral-Element Time Marching Methods for Phase-Field Nonlinear Gradient Systems
New energetic spectral-element time integrators for phase-field gradient systems that preserve discrete energy dissipation and mass conservation, with numerical tests showing better performance than BDF4 and ETDRK4 on Allen-Cahn problems.
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Justification and structure- and asymptotic-preserving discretizations of a hyperbolized Cahn-Hilliard equation
Develops energy-stable asymptotic-preserving discretizations of a hyperbolized Cahn-Hilliard equation via SBP operators and IMEX Runge-Kutta methods guided by relative-energy error estimates.