Piecewise Solenoidal Vector Fields and the Stokes Problem

Nonconforming finite element approximations to solutions of the Stokes equations are constructed. Optimal rates of convergence are proved for the velocity and pressure approximations. For the pressure approximation, C0piecewise polynomial functions are used. The class of vector fields used to approx...

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Bibliographic Details
Published in:SIAM journal on numerical analysis 1990-12, Vol.27 (6), p.1466-1485
Main Authors: Baker, Garth A., Jureidini, Wadi N., Karakashian, Ohannes A.
Format: Article
Language:English
Subjects:
Applied mathematics
Approximation
Boundary value problems
Estimates
Exact sciences and technology
Finite element method
Incompressibility
Incompressible vector fields
Integers
Lagrange multiplier
Mathematical functions
Mathematics
Numerical analysis
Numerical analysis. Scientific computation
Partial differential equations, boundary value problems
Polynomials
Sciences and techniques of general use
Triangulation
Vector fields
Vector valued functions
Velocity
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Description
Summary:Nonconforming finite element approximations to solutions of the Stokes equations are constructed. Optimal rates of convergence are proved for the velocity and pressure approximations. For the pressure approximation, C0piecewise polynomial functions are used. The class of vector fields used to approximate the velocity field have piecewise polynomial components, discontinuous across interelement boundaries. On each "triangle" these vector fields satisfy the incompressibility condition pointwise. It is shown that these piecewise solenoidal vector fields possess optimal approximation properties to smooth solenoidal vector fields on domains with curved boundaries.
ISSN:0036-1429
1095-7170
DOI:10.1137/0727085