FULLY-DISCRETE FINITE ELEMENT APPROXIMATION FOR A FAMILY OF DEGENERATE PARABOLIC PROBLEMS | Zendy

Ramiro Acevedo | Zendy; Christian Gómez | Zendy; Bibiana López-Rodríguez | Zendy

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FULLY-DISCRETE FINITE ELEMENT APPROXIMATION FOR A FAMILY OF DEGENERATE PARABOLIC PROBLEMS

Author(s) -

Ramiro Acevedo,

Christian Gómez,

Bibiana López-Rodríguez

Publication year - 2022

Publication title -

mathematical modelling and analysis

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 0.491

H-Index - 25

eISSN - 1648-3510

pISSN - 1392-6292

DOI - 10.3846/mma.2022.12846

Subject(s) - degenerate energy levels , mathematics , finite element method , convergence (economics) , space (punctuation) , scheme (mathematics) , parabolic partial differential equation , mathematical analysis , computer science , partial differential equation , physics , quantum mechanics , economics , thermodynamics , economic growth , operating system

The aim of this work is to show an abstract framework to analyze the numerical approximation by using a finite element method in space and a BackwardEuler scheme in time of a family of degenerate parabolic problems. We deduce sufficient conditions to ensure that the fully-discrete problem has a unique solution and to prove quasi-optimal error estimates for the approximation. Finally, we show a degenerate parabolic problem which arises from electromagnetic applications and deduce its well-posedness and convergence by using the developed abstract theory, including numerical tests to illustrate the performance of the method and confirm the theoretical results.

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