On the finite element method for a nonlocal degenerate parabolic problem

On the finite element method for a nonlocal degenerate parabolic problem

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 soluti...

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Veröffentlicht in:Computers & mathematics with applications (1987) 2017-04, Vol.73 (8), p.1724-1740
Hauptverfasser: Almeida, Rui M.P., Antontsev, Stanislav N., Duque, José C.M.
Format: Artikel
Sprache:eng
Schlagworte:
Degenerate
Finite element
Finite element analysis
Finite element method
Galerkin method
Nonlinear equations
Nonlocal
Numerical analysis
Parabolas
Parabolic
PDE
Studies
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Beschreibung
Zusammenfassung: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.
ISSN:0898-1221
1873-7668
DOI:10.1016/j.camwa.2017.02.013