Open AccessFULLY-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/mathematical modeling 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.