Fast Algorithm Based on TT-M FE Method for Allen-Cahn Equation

East Asian Journal on Applied Mathematics
Vol. 10 No. 2 (2020), pp. 316-337
DOI: 10.4208/eajam.260119.220719
Preview Buy Article · USD $15 Full text requires purchase or subscription
Author(s)
, , ,
    Hongen Jia
    Department of Mathematics, Taiyuan University of Technology, 030024 Taiyuan, China. Taiyuan Univ Technol, Dept Math, Taiyuan 030024, Peoples R China
    Search all author publications
1 google
2 Taiyuan Univ Technol, Dept Math, Taiyuan 030024, Peoples R China
3 Department of Mathematics, Taiyuan University of Technology, 030024 Taiyuan, China.
Received
January 26, 2019
Accepted
July 22, 2019
Abstract

A fast time two-mesh finite element algorithm using coarse and fine meshes is applied to the nonlinear Allen-Cahn equation. The stability and convergence of the method are studied and detailed error estimates are provided. Numerical examples confirm the theoretical results. Traditional Galerkin finite element and time two-mesh finite element methods are compared with respect to CPU time, accuracy and coarsening processing. Numerical experiments show the efficiency and effectiveness of the fast algorithm proposed.

Keywords
Fast algorithm time two-mesh finite element method Allen-Cahn equation stability convergence.
More from this issue
Using Parity to Accelerate the Computation of the Zeros of Truncated Legendre and Gegenbauer Polynomial Series and Gaussian Quadrature
P. Boyd
pp. 217-242
The Dynamics of Lump, Lumpoff and Rogue Wave Solutions of (2+1)-Dimensional Hirota-Satsuma-Ito Equations
Zhang et al.
pp. 243-255
Numerical Methods for $Q$-Weighted Nonnegative Matrix Tri-Factorization
Li et al.
pp. 256-273
A Jacobi-Galerkin Spectral Method for Computing the Ground and First Excited States of Nonlinear Fractional Schrödinger Equation
Ma et al.
pp. 274-294
Stay updated
Share
How to Cite
RIS BibTeX