Pointwise error estimates for a generalized Oseen problem and an application to an optimal control problem | Zendy

Allendes Alejandro | Zendy; Campaña Gilberto | Zendy; Hernández Erwin | Zendy

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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.

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