The Euler-Galerkin finite element method for nonlocal diffusion problems with a p-Laplace-type operator

ABSTRACT

This paper is devoted to the study of the finite element method for a class of non-linear nonlocal diffusion problems associated with p-Laplace-type operator. Using the Euler–Galerkin finite element method, the convergence and a priori error estimates for the semi-discrete as well as fully-discrete formulations are established.

KEYWORDS:

• Nonlocal diffusion term
• p-Laplace operator
• optimal error estimate
• Euler scheme
• Galerkin finite-element method

AMS SUBJECT CLASSIFICATIONS:

• 65N12
• 65N30
• 35K65
• 35J65

Acknowledgements

The author would like to thank the referees for their constructive remarks which help improve this work.

Notes

No potential conflict of interest was reported by the author.