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http://hdl.handle.net/10397/89357
| Title: | Energy-decaying extrapolated RK-SAV methods for the Allen–Cahn and Cahn–Hilliard equations | Authors: | Akrivis, G Li, B Li, D |
Issue Date: | 2019 | Source: | SIAM journal on scientific computing, 2019, v. 41, no. 6, p. A3703-A3727 | 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. | Keywords: | Algebraic stability Allen–Cahn equation Cahn–Hilliard equation Energy decay Extrapolation Gauss methods Radau IIA methods Runge–Kutta methods Scalar auxiliary variable |
Publisher: | Society for Industrial and Applied Mathematics | Journal: | SIAM journal on scientific computing | ISSN: | 1064-8275 | EISSN: | 1095-7197 | DOI: | 10.1137/19M1264412 | Rights: | © 2019, Society for Industrial and Applied Mathematics. Posted with permission of the publisher. The following publication Akrivis, G., Li, B., & Li, D. (2019). Energy-decaying extrapolated RK-SAV methods for the Allen–Cahn and Cahn–Hilliard equations. SIAM Journal on Scientific Computing, 41(6), A3703-A3727 is available at https://dx.doi.org/10.1137/19M1264412 |
| Appears in Collections: | Journal/Magazine Article |
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| 19m1264412.pdf | 512.66 kB | Adobe PDF | View/Open |
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