Method of Lines Transpose: Energy Gradient Flows Using Direct Operator Inversion for Phase-Field Models

DOI10.1137/16M1104123zbMath1407.65155arXiv1611.04214MaRDI QIDQ5372662

Hana Cho, Matthew F. Causley, Andrew J. Christlieb

Publication date: 27 October 2017

Published in: SIAM Journal on Scientific Computing (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1611.04214

zbMATH Keywords

Rothe's methodCahn-HilliardADI schemesalternating direction implicit methodsimplicit methodsfunctionalized Cahn-Hilliardboundary integral methodsmethod of lines transposeunconditionally gradient stable schemes

Mathematics Subject Classification ID

Finite difference methods for initial value and initial-boundary value problems involving PDEs (65M06) Stability and convergence of numerical methods for initial value and initial-boundary value problems involving PDEs (65M12) Spectral, collocation and related methods for initial value and initial-boundary value problems involving PDEs (65M70) Method of lines for initial value and initial-boundary value problems involving PDEs (65M20) Boundary element methods for initial value and initial-boundary value problems involving PDEs (65M38) Fundamental solutions, Green's function methods, etc. for initial value and initial-boundary value problems involving PDEs (65M80)

Related Items (8)

Numerical comparison of modified-energy stable SAV-type schemes and classical BDF methods on benchmark problems for the functionalized Cahn-Hilliard equation ⋮ A kernel based high order ``explicit unconditionally stable scheme for time dependent Hamilton-Jacobi equations ⋮ A kernel-based explicit unconditionally stable scheme for Hamilton-Jacobi equations on nonuniform meshes ⋮ Parallel algorithms for successive convolution ⋮ Unconditionally energy stable second-order numerical schemes for the functionalized Cahn-Hilliard gradient flow equation based on the SAV approach ⋮ A Kernel Based Unconditionally Stable Scheme for Nonlinear Parabolic Partial Differential Equations ⋮ Highly accurate, linear, and unconditionally energy stable large time-stepping schemes for the functionalized Cahn-Hilliard gradient flow equation ⋮ Kernel based high order ``explicit unconditionally stable scheme for nonlinear degenerate advection-diffusion equations

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