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Pressure Approximation (pressure + approximation)

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Engineering75%

Selected Abstracts

On the quadrilateral Q2,P1 element for the Stokes problem

INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN FLUIDS, Issue 11 2002
Daniele Boffi
Abstract The Q2 , P1 approximation is one of the most popular Stokes elements. Two possible choices are given for the definition of the pressure space: one can either use a global pressure approximation (that is on each quadrilateral the finite element space is spanned by 1 and by the global co-ordinates x and y) or a local approach (consisting in generating the local space by means of the constants and the local curvilinear co-ordinates on each quadrilateral , and ,). The former choice is known to provide optimal error estimates on general meshes. This has been shown, as it is standard, by proving a discrete inf,sup condition. In the present paper we check that the latter approach satisfies the inf,sup condition as well. However, recent results on quadrilateral finite elements bring to light a lack in the approximation properties for the space coming out from the local pressure approach. Numerical results actually show that the second choice (local or mapped pressure approximation) is suboptimally convergent. Copyright © 2002 John Wiley & Sons, Ltd. [source]

A new class of stabilized mesh-free finite elements for the approximation of the Stokes problem

NUMERICAL METHODS FOR PARTIAL DIFFERENTIAL EQUATIONS, Issue 5 2004
V. V. K. Srinivas Kumar
Abstract Previously, we solved the Stokes problem using a new linear - constant stabilized mesh-free finite element based on linear Weighted Extended B - splines (WEB-splines) as shape functions for the velocity approximation and constant extended B-splines for the pressure (Kumar et al., 2002). In this article we derive another linear-constant element that uses the Haar wavelets for the pressure approximation and a quadratic - linear element that uses quadrilateral bubble functions for the enrichment of the velocity approximation space. The inf-sup condition or Ladyshenskaya-Babus,ka-Brezzi (LBB) condition is verified for both the elements. The main advantage of these new elements over standard finite elements is that they use regular grids instead of irregular partitions of domain, thus eliminating the difficult and time consuming pre-processing step. Convergence and condition number estimates are derived. Numerical experiments in two space dimensions confirm the theoretical predictions. © 2004 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq, 2004. [source]

Stability of a trilinear,trilinear approximation for the Stokes equations

INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN BIOMEDICAL ENGINEERING, Issue 5 2003
Kamel Nafa
Abstract The choice of mixed finite element approximations for fluid flow problems is a compromise between accuracy and computational efficiency. Although a number of finite elements are found in the literature only few low-order approximations are stable. This is particularly true for three-dimensional flow problems. These elements are attractive because of their simplicity and efficiency, but can suffer though poor rate of convergence. In this paper the stability of a continuous trilinear,trilinear approximation is being analysed for general geometries. Using the macroelement technique, we prove the stability of the approximation. As a result, optimal rates of convergence are obtained for both the velocity and pressure approximations. Copyright © 2003 John Wiley & Sons, Ltd. [source]