Arbitrarily High Order and Fully Discrete Extrapolated RK-SAV/DG Schemes for Phase-field Gradient Flows

Tang, Tao1,2; Wu, Xu3,4; Yang, Jiang4,5

2022-11-01

10.1007/s10915-022-01995-5

JOURNAL OF SCIENTIFIC COMPUTING   Impact Factor & Quartile

0885-7474

1573-7691

In this paper, we construct and analyze a fully discrete method for phase-field gradient flows, which uses extrapolated Runge-Kutta with scalar auxiliary variable (RK-SAV) method in time and discontinuous Galerkin (DG) method in space. We propose a novel technique to decouple the system, after which only several elliptic scalar problems with constant coefficients need to be solved independently. Discrete energy decay property of the method is proved for gradient flows. The scheme can be of arbitrarily high order both in time and space, which is demonstrated rigorously for the Allen-Cahn equation and the Cahn-Hilliard equation. More precisely, optimal L-2-error bound in space and qth-order convergence rate in time are obtained for q-stage extrapolated RK-SAV/DG method. Several numerical experiments are carried out to verify the theoretical results.

Phase-field models Gradient flows Energy stability Convergence and error analysis Allen-Cahn equation Cahn-Hilliard equation

SCI

English

Corresponding

National Science Foundation of China["NSFC-11871264","NSFC/RGC 11961160718"] ; Hong Kong RGC[NSFC/RGC 11961160718] ; Guangdong Provincial Key Laboratory of Computational Science and Material Design[2019B030301001] ; Shenzhen Natural Science Fund[RCJC20210609103819018]

Mathematics

Mathematics, Applied

WOS:000854593400003

SPRINGER/PLENUM PUBLISHERS

MATHEMATICS

Web of Science

1.BNU HKBU United Int Coll, Div Sci & Technol, Zhuhai, Guangdong, Peoples R China
2.Southern Univ Sci & Technol, SUSTech Int Ctr Math, Shenzhen, Peoples R China
3.Harbin Inst Technol, Sch Math, Harbin, Peoples R China
4.Southern Univ Sci & Technol, Dept Math, Shenzhen, Peoples R China
5.Southern Univ Sci & Technol, Guangdong Prov Key Lab Computat Sci & Mat Design, Shenzhen, Peoples R China

Tang, Tao,Wu, Xu,Yang, Jiang. Arbitrarily High Order and Fully Discrete Extrapolated RK-SAV/DG Schemes for Phase-field Gradient Flows[J]. JOURNAL OF SCIENTIFIC COMPUTING,2022,93(2).

Tang, Tao,Wu, Xu,&Yang, Jiang.(2022).Arbitrarily High Order and Fully Discrete Extrapolated RK-SAV/DG Schemes for Phase-field Gradient Flows.JOURNAL OF SCIENTIFIC COMPUTING,93(2).

Tang, Tao,et al."Arbitrarily High Order and Fully Discrete Extrapolated RK-SAV/DG Schemes for Phase-field Gradient Flows".JOURNAL OF SCIENTIFIC COMPUTING 93.2(2022).