Fully-discrete finite element approximation for a family of degenerate parabolic problems

• Published in: Mathematical modelling and analysis Vol. 27; no. 1; pp. 134 - 160
• Main Authors: Acevedo, Ramiro, Gómez, Christian, López-Rodríguez, Bibiana
• Format: Journal Article
• Language: English
• Published: Vilnius Vilnius Gediminas Technical University 07.02.2022
• Subjects: Approximation; backward euler scheme; eddy current model; Electromagnetism; error estimates; Finite element method; fully-discrete approximation; Mathematical analysis; parabolic degenerate equations; parabolic-elliptic equations; Colombia; parabolic degenerate equations; finite element method; parabolic-elliptic equations; backward Euler scheme; eddy current model; error estimates; fully-discrete approximation
• ISSN: 1392-6292; 1648-3510
• DOI: 10.3846/mma.2022.12846

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.