On the finite element method for a nonlocal degenerate parabolic problem

2014/09/30 by Rui M.P. Almeida, Almeida, Rui M. P., S. N. Antont︠s︡ev +3
Engineering · Mathematics · #Advanced Numerical Methods in Computational Mathematics #Differential Equations and Boundary Problems #Differential Equations and Numerical Methods #FOS: Mathematics #Numerical Analysis (math.NA)

paper · pdf · doi:10.48550/arxiv.1409.8453

openalex publication_date 2014/09/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

The aim of this paper is the numerical study of a class of nonlinear nonlocal degenerate parabolic equations. The convergence and error bounds of the solutions are proved for a linearized Crank-Nicolson-Galerkin finite element method with polynomial approximations of degree k≥ 1. Some explicit solutions are obtained and used to test the implementation of the method in Matlab environment.

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