WEB-Spline-based mesh-free finite element approximation for p-Laplacian

Abstract

In this paper, we discuss the approximation of p-Laplace problem using WEB-Spline based mesh free finite elements. Along with usual weak formulation, we also consider the mixed formulation of the p-Laplace problem. We give existence, uniqueness results for both continuous and discrete problems. We also provide a priori error estimates for both the formulations.

Keywords:

• meshless method
• WEB-Spline
• inf-Sup Condition
• p-Laplacian

2000 AMS Subject Classifications:

• 65N12
• 65N15
• 65N22
• 65N30

Acknowledgments

The authors acknowledge anonymous reviewers for many helpful suggestions and comments. Also, the authors would like to thank Prof. Klaus H$\ddot{o}$llig for his help and suggestions during implementation to WEB-Spline method for p-Laplace problem.

Disclosure statement

No potential conflict of interest was reported by the authors.