A New Mixed Finite Element for the Stokes and Elasticity Problems
- 1 August 1993
- journal article
- Published by Society for Industrial & Applied Mathematics (SIAM) in SIAM Journal on Numerical Analysis
- Vol. 30 (4) , 971-990
- https://doi.org/10.1137/0730051
Abstract
The Stokes problem is approximated by a mixed finite element method using a new finite element, which has properties analogous to the finite volume methods, namely, the local conservation of the momentum and the mass. Estimates of optimal order are derived for the errors in the velocity, the pressure, and the gradient of the velocity. This new finite element also works for the elasticity problem, and all estimates are valid uniformly with respect to the compressibility. Finally, some numerical results for the incompressible Navier–Stokes equations are presented.Keywords
This publication has 13 references indexed in Scilit:
- A mixed finite element method for the Stokes equationsNumerical Methods for Partial Differential Equations, 1994
- Mixed and Hybrid Finite Element MethodsPublished by Springer Nature ,1991
- Mathematical derivation of a finite volume formulation for laminar flow in complex geometriesInternational Journal for Numerical Methods in Fluids, 1989
- A new mixed formulation for elasticityNumerische Mathematik, 1988
- Finite Element Methods for Navier-Stokes EquationsPublished by Springer Nature ,1986
- A family of higher order mixed finite element methods for plane elasticityNumerische Mathematik, 1984
- Mixed finite elements in ?3Numerische Mathematik, 1980
- Unconditionally stable explicit methods for parabolic equationsNumerische Mathematik, 1980
- New finite element results for the square cavityComputers & Fluids, 1979
- Error-bounds for finite element methodNumerische Mathematik, 1971