Error Estimates on a Stable and Reliable Numerical Scheme for a Fully Discrete Time-Dependent Allen-Cahn Equation

Authors

Pius W. M. Chin, Department of Mathematics and Applied Mathematics, University of Pretoria, Pretoria 0002, South AfricaFollow

Author Country (or Countries)

South Africa

Abstract

The stability analysis and error estimates are some of the well-known techniques carried out on a number of commonly used numerical schemes for Allen-Cahn equation. We exploit these techniques and design a reliable fully-discrete scheme consisting of coupling the Non-standard finite difference with the finite element method. We show that the solution obtained from this scheme is stabled and attains its optimal rate of convergence in both the H1 and L2-norms. We further show that this scheme replicates the properties of the exact solution. Some numerical experiments are performed to support our theoretical analysis.

Digital Object Identifier (DOI)

http://dx.doi.org/10.18576/amis/100418

Recommended Citation

W. M. Chin, Pius (2016) "Error Estimates on a Stable and Reliable Numerical Scheme for a Fully Discrete Time-Dependent Allen-Cahn Equation," Applied Mathematics & Information Sciences: Vol. 10: Iss. 4, Article 18.
DOI: http://dx.doi.org/10.18576/amis/100418
Available at: https://digitalcommons.aaru.edu.jo/amis/vol10/iss4/18