Publication: A posteriori error analysis of a momentum conservative Banach spaces based mixed-FEM for the Navier-Stokes problem
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Date
2022
Authors
Dra. Camaño-Valenzuela, Jessika
Dr. Caucao-Paillán, Sergio
Oyarzúa, Ricardo
Villa-Fuentes, Segundo
Journal Title
Journal ISSN
Volume Title
Publisher
Applied Numerical Mathematics
Abstract
In this paper we develop an a posteriori error analysis of a new momentum conservative mixed finite element method recently introduced for the steady-state Navier–Stokes problem in two and three dimensions. More precisely, by extending standard techniques commonly used on Hilbert spaces to the case of Banach spaces, such as local estimates, and suitable Helmholtz decompositions, we derive a reliable and efficient residual-based a posteriori error estimator for the corresponding mixed finite element scheme on arbitrary (convex or non-convex) polygonal and polyhedral regions. On the other hand, inverse inequalities, the localization technique based on bubble functions, among other tools, are employed to prove the efficiency of the proposed a posteriori error indicator. Finally, several numerical results confirming the properties of the estimator and illustrating the performance of the associated adaptive algorithm are reported.
Description
Keywords
Navier–Stokes, Momentum conservativity, Mixed finite element method, Banach spaces, Raviart–Thomas elements, A posteriori, Reliability, Efficiency