Effective numerical computation of p(x)–Laplace equations in 2D

Abstract

In this article we implement a method for the computation of a nonlinear elliptic problem with nonstandard growth driven by the $p(x)-$Laplacian operator. Our implementation is based in the decomposition–coordination method that allows us, via an iterative process, to solve in each step a linear differential equation and a nonlinear algebraic equation. Our code is implemented in MatLab in two dimensions and turns out to be extremely efficient from the computational point of view.

Keywords:

• $p(x)-$Laplacian
• finite elements
• decomposition-coordination method

2010 Mathematics Subject Classifications:

• 65N30
• 35J92

Acknowledgments

The authors want to thank I. Ojea for some useful discussions and the help provided in an early version of the code. The authors also want to thank both referees for their helpful comments and insights on the paper that help us to improve the presentation of the results, in particular their comments with respect to the stopping criteria.

Disclosure statement

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

Additional information

Funding

JFB is supported by CONICET PIP No. 11220150100032CO and by ANPCyT, PICT 2016-1022 and is a member of CONICET