Analysis of locally stabilized mixed finite element methods for the Stokes problem-Reference-Cited by-同舟云学术

Analysis of locally stabilized mixed finite element methods for the Stokes problem

Published:1992 Issue:197 Volume:58 Page:1-10
ISSN:0025-5718
Container-title:Mathematics of Computation
language:en
Short-container-title:Math. Comp.

Author:

Kechkar Nasserdine,Silvester David

Abstract

In this paper, a locally stabilized finite element formulation of the Stokes problem is analyzed. A macroelement condition which is sufficient for the stability of (locally stabilized) mixed methods based on a piecewise constant pressure approximation is introduced. By satisfying this condition, the stability of the Q 1 − P 0 {Q_1} - {P_0} quadrilateral, and the P 1 − P 0 {P_1} - {P_0} triangular element, can be established.

Publisher

American Mathematical Society (AMS)

Subject

Applied Mathematics,Computational Mathematics,Algebra and Number Theory

Link

http://www.ams.org/mcom/1992-58-197/S0025-5718-1992-1106973-X/S0025-5718-1992-1106973-X.pdf

Reference16 articles.

1. Error-bounds for finite element method;Babuška, Ivo;Numer. Math.,1970

2. Analysis of mixed methods using mesh dependent norms;Babuška, I.;Math. Comp.,1980

3. Stability of finite elements under divergence constraints;Boland, J. M.;SIAM J. Numer. Anal.,1983

4. A preconditioning technique for indefinite systems resulting from mixed approximations of elliptic problems;Bramble, James H.;Math. Comp.,1988

5. F. Brezzi and J. Pitkäranta, On the stabilisation of finite element approximations of the Stokes problem, Efficient Solutions of Elliptic Systems (W. Hackbusch, ed.), Notes on Numerical Fluid Mechanics, vol. 10, Vieweg, Braunschweig, 1984, pp. 11-19.

Cited by 109 articles. 订阅此论文施引文献订阅此论文施引文献，注册后可以免费订阅5篇论文的施引文献，订阅后可以查看论文全部施引文献

1. High order compact augmented methods for Stokes equations with different boundary conditions;Computer Physics Communications;2024-08

2. A review of VMS a posteriori error estimation with emphasis in fluid mechanics;Computer Methods in Applied Mechanics and Engineering;2023-12

3. Robin-type domain decomposition with stabilized mixed approximation for incompressible flow;Computers & Mathematics with Applications;2023-10

4. Analysis and preconditioning of parameter-robust finite element methods for Biot’s consolidation model;BIT Numerical Mathematics;2023-07-25

5. A novel stabilized P1 × P0 finite element formulation for the time-dependent incompressible Navier–Stokes equations;AIP Advances;2023-07-01