Please use this identifier to cite or link to this item:
http://hdl.handle.net/10397/89358
Title: | Arbitrarily high-order exponential cut-off methods for preserving maximum principle of parabolic equations | Authors: | Li, B Yang, J Zhou, Z |
Issue Date: | 2020 | Source: | SIAM journal on scientific computing, 2020, v. 42, no. 6, p. A3957-A3968 | Abstract: | A new class of high-order maximum principle preserving numerical methods is proposed for solving parabolic equations, with application to the semilinear Allen-Cahn equation. The proposed method consists of a kth-order multistep exponential integrator in time and a lumped mass finite element method in space with piecewise rth-order polynomials and Gauss-Lobatto quadrature. At every time level, the extra values violating the maximum principle are eliminated at the finite element nodal points by a cut-off operation. The remaining values at the nodal points satisfy the maximum principle and are proved to be convergent with an error bound of O(τ k + hr). The accuracy can be made arbitrarily high-order by choosing large k and r. Extensive numerical results are provided to illustrate the accuracy of the proposed method and the effectiveness in capturing the pattern of phase-field problems. | Keywords: | Allen-Cahn equation Cut-off Exponential integrator High order Lumped mass Maximum principle Parabolic equation |
Publisher: | Society for Industrial and Applied Mathematics | Journal: | SIAM journal on scientific computing | ISSN: | 1064-8275 | EISSN: | 1095-7197 | DOI: | 10.1137/20M1333456 | Rights: | © 2020, Society for Industrial and Applied Mathematics. Unauthorized reproduction of this article is prohibited. First Published in SIAM Journal on SIAM Journal on Scientific Computing in Volume 42, Issue 6, published by the Society for Industrial and Applied Mathematics (SIAM) |
Appears in Collections: | Journal/Magazine Article |
Files in This Item:
File | Description | Size | Format | |
---|---|---|---|---|
a0602-n06_cut_off_rev.pdf | Pre-Published version | 783.95 kB | Adobe PDF | View/Open |
Page views
44
Last Week
2
2
Last month
Citations as of Oct 1, 2023
Downloads
4
Citations as of Oct 1, 2023
SCOPUSTM
Citations
29
Citations as of Sep 28, 2023
WEB OF SCIENCETM
Citations
29
Citations as of Sep 28, 2023

Google ScholarTM
Check
Altmetric
Items in DSpace are protected by copyright, with all rights reserved, unless otherwise indicated.