Isogeometric method for a nonlocal degenerate parabolic problem

Abstract

In this article, we apply NURBS-based isogeometric method to solve a nonlocal degenerate parabolic problem. The isogeometric method has advantages over classical finite element method in terms of exact geometry representation and higher order smooth basis functions. We consider the NURBS-based semi-discretization of the problem. The second-order Crank–Nicolson method is applied for the complete discretization of the problem. Error estimates of the semi-discrete and fully-discrete problems are derived. Few numerical examples are provided to verify the theoretical findings.

Keywords:

• Isogeometric method
• degenerate
• nonlocal
• parabolic PDEs

2020 Mathematics Subject Classification:

• 00A69

Acknowledgments

The authors acknowledge anonymous reviewers for many helpful suggestions and comments. The first author also would like to express gratitude to the Department of Science and Technology (DST), New Delhi, India, for providing INSPIRE Fellowship to carry out the research work.

Disclosure statement

No potential conflict of interest was reported by the author(s).

Additional information

Funding

This work was supported by Department of Science and Technology, Ministry of Science and Technology, India.