Minimization techniques for p(x)-Laplacian problem using WEB-Spline based mesh-free method

ABSTRACT

In this paper, we propose minimization techniques with WEB-Spline based mesh-free finite element method for the solution of $p\left(x\right)$-Laplacian problem. The WEB-Spline method uses weighted extended B-splines on a regular grid as basis functions and does not require any mesh generation which eliminates a difficult, time-consuming preprocessing step and accurate approximations are possible with relatively low-dimensional subspaces. We perform some numerical experiments to demonstrate the efficiency of the WEB-Spline method.

KEYWORDS:

• Meshless method
• WEB-Splines
• steepest descent method
• Quasi-Newton method
• $p\left(x\right)$-Laplacian

2010 AMS SUBJECT CLASSIFICATIONS:

• 65N12
• 65N22
• 65N30
• 41A15
• 35Q93

Acknowledgments

The authors would like to thank the referees for thoroughly reading the manuscript and their valuable suggestions.

Disclosure statement

No potential conflict of interest was reported by the authors.

Additional information

Funding

First author is thankful to University Grants Commission, India, for their financial support through Senior Research Fellowship (ID No. 421249).