Abstract
This article aims to solve the nonlinear Allen-Cahn equation numerically. The diagonally implicit fractional-step θ-(DIFST) scheme is used for the discretization of the time derivative term while the space derivative is discretized by the conforming finite element method. The computational efficiency of the DIFST scheme in terms of CPU time and temporal error estimation is computed and compared with other time discretization schemes. Several test problems are presented to show the effectiveness of the DIFST scheme.
| Original language | English |
|---|---|
| Pages (from-to) | 603-612 |
| Number of pages | 10 |
| Journal | International Journal of Nonlinear Sciences and Numerical Simulation |
| Volume | 23 |
| Issue number | 3 |
| DOIs | |
| State | Published - 1 Jun 2022 |
Bibliographical note
Publisher Copyright:© 2021 Walter de Gruyter GmbH, Berlin/Boston.
Keywords
- DUNE-PDELab
- diagonally implicit fractional-step θ-scheme
- finite element method (FEM)
- the Allen-Cahn equation
ASJC Scopus subject areas
- Statistical and Nonlinear Physics
- Computational Mechanics
- Modeling and Simulation
- Engineering (miscellaneous)
- Mechanics of Materials
- General Physics and Astronomy
- Applied Mathematics
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