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A stabilized mixed method applied to Stokes system with nonhomogeneous source terms: The stationary case Dedicated to Prof. R. Rodríguez, on the occasion of his 65th birthday
Author(s) -
Barrios Tomás P.,
Behrens Edwin M.,
Bustinza Rommel
Publication year - 2020
Publication title -
international journal for numerical methods in fluids
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.938
H-Index - 112
eISSN - 1097-0363
pISSN - 0271-2091
DOI - 10.1002/fld.4793
Subject(s) - a priori and a posteriori , estimator , mathematics , dirichlet boundary condition , dirichlet distribution , stokes problem , dual (grammatical number) , boundary (topology) , boundary value problem , algorithm , mathematical optimization , mathematical analysis , finite element method , engineering , philosophy , statistics , epistemology , art , literature , structural engineering
Summary This article is concerned with the Stokes system with nonhomogeneous source terms and nonhomogeneous Dirichlet boundary condition. First, we reformulate the problem in its dual mixed form, and then, we study its corresponding well‐posedness. Next, in order to circumvent the well‐known Babuška‐Brezzi condition, we analyze a stabilized formulation of the resulting approach. Additionally, we endow the scheme with an a posteriori error estimator that is reliable and efficient. Finally, we provide numerical experiments that illustrate the performance of the corresponding adaptive algorithm and support its use in practice.