A priori and a posteriori estimates for three‐dimensional Stokes equations with nonstandard boundary conditions | Zendy

Abboud Hyam | Zendy; El Chami Fida | Zendy; Sayah Toni | Zendy

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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

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