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A priori and a posteriori estimates for three‐dimensional Stokes equations with nonstandard boundary conditions
Author(s) -
Abboud Hyam,
El Chami Fida,
Sayah Toni
Publication year - 2012
Publication title -
numerical methods for partial differential equations
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.901
H-Index - 61
eISSN - 1098-2426
pISSN - 0749-159X
DOI - 10.1002/num.20676
Subject(s) - a priori and a posteriori , mathematics , stokes problem , boundary value problem , partial differential equation , curl (programming language) , finite element method , mathematical analysis , poisson distribution , boundary (topology) , poisson's equation , computer science , statistics , physics , programming language , epistemology , thermodynamics , philosophy
In this article, we study the Stokes problem with some nonstandard boundary conditions. The variational formulation decouples into a system for the velocity and a Poisson equation for the pressure. The corresponding discrete system do not need an inf‐sup condition. Hence, the velocity is approximated with “ curl ” conforming finite elements and the pressure with standard continuous elements. Next, we establish optimal a priori and a posteriori estimates and we finally concluded with numerical tests. © 2011 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq, 2012