A weak Galerkin finite element scheme for the Cahn-Hilliard equation
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- by Junping Wang, Qilong Zhai, Ran Zhang and Shangyou Zhang HTML | PDF
- Math. Comp. 88 (2019), 211-235 Request permission
Abstract:
This article presents a weak Galerkin (WG) finite element method for the Cahn-Hilliard equation. The WG method makes use of piecewise polynomials as approximating functions, with weakly defined partial derivatives (first and second order) computed locally by using the information in the interior and on the boundary of each element. A stabilizer is constructed and added to the numerical scheme for the purpose of providing certain weak continuities for the approximating function. A mathematical convergence theory is developed for the corresponding numerical solutions, and optimal order of error estimates are derived. Some numerical results are presented to illustrate the efficiency and accuracy of the method.References
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Additional Information
- Junping Wang
- Affiliation: Division of Mathematical Sciences, National Science Foundation, Arlington, Virginia 22230
- MR Author ID: 216677
- Email: jwang@nsf.gov
- Qilong Zhai
- Affiliation: Department of Mathematics, Jilin University, Changchun, China
- MR Author ID: 1114983
- Email: diql15@mails.jlu.edu.cn
- Ran Zhang
- Affiliation: Department of Mathematics, Jilin University, Changchun, China
- MR Author ID: 719427
- Email: zhangran@mail.jlu.edu.cn
- Shangyou Zhang
- Affiliation: Department of Mathematical Sciences, University of Delaware, Newark, Delaware 19716
- MR Author ID: 261174
- Email: szhang@udel.edu
- Received by editor(s): April 22, 2017
- Received by editor(s) in revised form: October 7, 2017, and March 20, 2018
- Published electronically: August 21, 2018
- Additional Notes: The research of the first author was supported in part by the NSF IR/D program, while working at National Science Foundation. However, any opinion, finding, and conclusions or recommendations expressed in this material are those of the author and do not necessarily reflect the views of the National Science Foundation.
The research of the third author was supported in part by China Natural National Science Foundation (U1530116,91630201,11471141), and by the Program for Cheung Kong Scholars of Ministry of Education of China, Key Laboratory of Symbolic Computation and Knowledge Engineering of Ministry of Education, Jilin University, Changchun, 130012, People’s Republic of China. - Journal: Math. Comp. 88 (2019), 211-235
- MSC (2010): Primary 65N30, 65N15, 65N12, 74N20; Secondary 35B45, 35J50, 35J35
- DOI: https://doi.org/10.1090/mcom/3369
- MathSciNet review: 3854056