Journal article
Numerical analysis of a parabolic hemivariational inequality for semipermeable media
Journal of computational and applied mathematics, Vol.389, 113326
06/2021
DOI: 10.1016/j.cam.2020.113326
Abstract
In this paper, we consider the numerical solution of a model problem in the form of a parabolic hemivariational inequality that arises in applications of semipermeable media. The model problem is first studied as a particular case of an abstract parabolic hemivariational inequality. A general fully discrete numerical method is introduced for the abstract parabolic hemivariational inequality, where the time derivative of the unknown solution is approximated by the backward divided difference. A Céa’s type inequality is shown as a preparation for error estimation. Then the general result is specialized for the numerical solution of the model problem and an optimal order error estimate with the use of linear finite elements is derived. Finally numerical examples are presented to show the performance of the numerical solutions and the emphasis is to illustrate numerical convergence orders that match the theoretically predicted optimal first order convergence of the linear element solutions with respect to the finite element mesh-size and the time step-size.
Details
- Title: Subtitle
- Numerical analysis of a parabolic hemivariational inequality for semipermeable media
- Creators
- Weimin Han - University of IowaCheng Wang - Tongji University
- Resource Type
- Journal article
- Publication Details
- Journal of computational and applied mathematics, Vol.389, 113326
- Publisher
- Elsevier B.V
- DOI
- 10.1016/j.cam.2020.113326
- ISSN
- 0377-0427
- eISSN
- 1879-1778
- Language
- English
- Date published
- 06/2021
- Academic Unit
- Mathematics
- Record Identifier
- 9984240860502771
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