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Pointwise error estimates for a generalized Oseen problem and an application to an optimal control problem
Author(s) -
Allendes Alejandro,
Campaña Gilberto,
Hernández Erwin
Publication year - 2019
Publication title -
mathematical methods in the applied sciences
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.719
H-Index - 65
eISSN - 1099-1476
pISSN - 0170-4214
DOI - 10.1002/mma.5597
Subject(s) - mathematics , pointwise , sobolev space , norm (philosophy) , interpolation (computer graphics) , pointwise convergence , convergence (economics) , finite element method , mathematical analysis , animation , approx , physics , computer graphics (images) , political science , computer science , law , economics , thermodynamics , economic growth , operating system
We derive pointwise error estimates for a generalized Oseen when it is approximated by a low order Taylor‐Hood finite element scheme in two dimensions. The analysis is based on estimates for regularized Green's functions associated with a generalized Oseen problem on weighted Sobolev spaces and weighted interpolation results. We apply the maximum norm results to obtain convergence in an optimal control problem governed by a generalized Oseen equation and present a numerical example that allows us to show the behavior of the error.