Name
Title | ||
|---|---|---|
Energy-Decaying Extrapolated RK--SAV Methods for the Allen--Cahn and Cahn--Hilliard Equations |
Abstract | ||
|---|---|---|
We construct and analyze a class of extrapolated and linearized Runge-Kutta (RK) methods, which can be of arbitrarily high order, for the time discretization of the Allen-Cahn and Cahn-Hilliard phase field equations, based on the scalar auxiliary variable (SAV) formulation. We prove that the proposed q-stage RK-SAV methods have qth-order convergence in time and satisfy a discrete version of the energy decay property. Numerical examples are provided to illustrate the discrete energy decay property and accuracy of the proposed methods. |
Year | DOI | Venue |
|---|---|---|
2019 | 10.1137/19M1264412 | SIAM JOURNAL ON SCIENTIFIC COMPUTING |
Keywords | Field | DocType |
Allen-Cahn equation,Cahn-Hilliard equation,energy decay,scalar auxiliary variable,Runge-Kutta methods,extrapolation,Gauss methods,Radau IIA methods,algebraic stability | Allen–Cahn equation,Discretization,Runge–Kutta methods,Mathematical analysis,Cahn–Hilliard equation,Extrapolation,Mathematics,Algebraic stability | Journal |
Volume | Issue | ISSN |
41 | 6 | 1064-8275 |
Citations | PageRank | References |
2 | 0.37 | 0 |
Authors | ||
3 | ||
Name | Order | Citations | PageRank |
|---|---|---|---|
| Georgios Akrivis | 1 | 158 | 32.43 |
| Buyang Li | 2 | 170 | 21.10 |
| Dongfang Li | 3 | 106 | 15.34 |