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Volume 10, Issue 2
Fast Algorithm Based on TT-M FE Method for Allen-Cahn Equation

Danxia Wang, Qingqing Du, Lingxiong Meng & Hongen Jia

DOI: 10.4208/eajam.260119.220719

East Asian J. Appl. Math., 10 (2020), pp. 316-337.

Published online: 2020-04

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  • 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.

  • AMS Subject Headings

35Q30, 74S05

  • Copyright

COPYRIGHT: © Global Science Press

  • Email address

danxia.wang@163. om (Danxia Wang)

992495866@qq. com (Qingqing Du)

menglingxiong@tyut.edu. cn (Lingxiong Meng)

jiahongen@tyut.edu. cn (Hongen Jia)

  • BibTex
  • RIS
  • TXT
@Article{EAJAM-10-316, author = {Wang , DanxiaDu , QingqingMeng , Lingxiong and Jia , Hongen}, title = {Fast Algorithm Based on TT-M FE Method for Allen-Cahn Equation}, journal = {East Asian Journal on Applied Mathematics}, year = {2020}, volume = {10}, number = {2}, pages = {316--337}, 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.

}, issn = {2079-7370}, doi = {https://doi.org/10.4208/eajam.260119.220719 }, url = {http://global-sci.org/intro/article_detail/eajam/16129.html} }
TY - JOUR T1 - Fast Algorithm Based on TT-M FE Method for Allen-Cahn Equation AU - Wang , Danxia AU - Du , Qingqing AU - Meng , Lingxiong AU - Jia , Hongen JO - East Asian Journal on Applied Mathematics VL - 2 SP - 316 EP - 337 PY - 2020 DA - 2020/04 SN - 10 DO - http://doi.org/10.4208/eajam.260119.220719 UR - https://global-sci.org/intro/article_detail/eajam/16129.html KW - Fast algorithm, time two-mesh finite element method, Allen-Cahn equation, stability, convergence. AB -

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.

Wang , DanxiaDu , QingqingMeng , Lingxiong and Jia , Hongen. (2020). Fast Algorithm Based on TT-M FE Method for Allen-Cahn Equation. East Asian Journal on Applied Mathematics. 10 (2). 316-337. doi:10.4208/eajam.260119.220719
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