Fully discrete finite element approximation for a family of degenerate parabolic mixed equations

2020/09/05 by Ramiro Acevedo, Acevedo, Ramiro, Christian Gómez +3
Computer Science · Engineering · Mathematics · #Advanced Mathematical Modeling in Engineering #Advanced Numerical Methods in Computational Mathematics #Differential Equations and Numerical Methods #FOS: Mathematics #Numerical Analysis (math.NA) #cs.NA #math.NA

paper · pdf · doi:10.48550/arxiv.2009.02607

29 pages, 9 figures

arxiv created 2020/09/05 · openalex publication_date 2020/09/05 · arxiv updated 2020/09/08 · openalex created_date 2022/07/25 · openalex updated_date 2026/07/28

Abstract

The aim of this work is to show an abstract framework to analyze the numerical approximation for a family of linear degenerate parabolic mixed equations by using a finite element method in space and a Backward-Euler scheme in time. We consider sufficient conditions to prove that the fully-discrete problem has a unique solution and prove quasi-optimal error estimates for the approximation. Furthermore, we show that mixed finite element formulations arising from dynamics fluids (time-dependent Stokes problem) and from electromagnetic applications (eddy current models), can be analyzed as applications of the developed theory. Finally, we include numerical tests to illustrate the performance of the method and confirm the theoretical results.

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