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

Danxia Wang, Qingqing Du, Lingxiong Meng & Hongen Jia

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 meshesis 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
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@Article{EAJAM-10-316, author = {Wang , Danxia and Du , Qingqing and Meng , 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 meshesis 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://dor.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 meshesis 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.

Danxia Wang, Qingqing Du, Lingxiong Meng & Hongen Jia. (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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