首页|High order accurate in time, fourth order finite difference schemes for the harmonic mapping flow

High order accurate in time, fourth order finite difference schemes for the harmonic mapping flow

扫码查看
原文链接
  • NSTL
  • Elsevier
In this paper, a fully discrete numerical scheme is proposed and analyzed for the harmonic mapping flow, with the fourth order spatial accuracy and higher than third order temporal accuracy. The fourth order spatial accuracy is realized via a long stencil finite difference, and the boundary extrapolation is implemented by making use of higher order Taylor expansion. Meanwhile, the high order (third or fourth order) temporal accuracy is based on a semi-implicit algorithm, which uses a combination of explicit Adams-Bashforth extrapolation for the nonlinear terms and implicit Adams-Moulton interpolation for the viscous diffusion term, with the corresponding integration formula coefficients. Both the consistency, linearized stability analysis and optimal rate convergence estimate (in the l(infinity) (0, T; l(2)) boolean AND l(2) (0, T; H-h(l)) norm) are provided. A few numerical examples are also presented in this article. (C) 2021 Elsevier B.V. All rights reserved.

Harmonic mapping flowThird order multi-step schemeFourth order long stencil difference approximationOptimal rate convergence analysisENERGY STABLE SCHEMETHIN-FILM MODELCONVERGENCE ANALYSISNUMERICAL SCHEMEHEAT-FLOWPRIMITIVE EQUATIONS2ND-ORDERCAHNEXISTENCEALGORITHM

Xia, Zeyu、Wang, Cheng、Xu, Liwei、Zhang, Zhengru

展开 >

Univ Elect Sci & Technol China

Univ Massachusetts

Beijing Normal Univ

2022

10.1016/j.cam.2021.113766

Journal of Computational and Applied Mathematics

Journal of Computational and Applied Mathematics

EISCI
ISSN：0377-0427
年,卷(期)：2022.401
  • 46