A new family of stable mixed finite elements for the 3D Stokes equations

Author:
Shangyou Zhang

Journal:
Math. Comp. **74** (2005), 543-554

MSC (2000):
Primary 65N30, 65F10

DOI:
https://doi.org/10.1090/S0025-5718-04-01711-9

Published electronically:
August 31, 2004

MathSciNet review:
2114637

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Abstract | References | Similar Articles | Additional Information

Abstract: A natural mixed-element approach for the Stokes equations in the velocity-pressure formulation would approximate the velocity by continuous piecewise-polynomials and would approximate the pressure by discontinuous piecewise-polynomials of one degree lower. However, many such elements are unstable in 2D and 3D. This paper is devoted to proving that the mixed finite elements of this - type when satisfy the stability condition--the Babuska-Brezzi inequality on macro-tetrahedra meshes where each big tetrahedron is subdivided into four subtetrahedra. This type of mesh simplifies the implementation since it has no restrictions on the initial mesh. The new element also suits the multigrid method.

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Additional Information

**Shangyou Zhang**

Affiliation:
Department of Mathematical Sciences, University of Delaware, Newark, Delaware 19716

Email:
szhang@math.udel.edu

DOI:
https://doi.org/10.1090/S0025-5718-04-01711-9

Keywords:
Stokes problem,
finite element,
mixed element,
inf-sup condition,
multigrid method

Received by editor(s):
October 3, 2002

Received by editor(s) in revised form:
January 9, 2003

Published electronically:
August 31, 2004

Article copyright:
© Copyright 2004
American Mathematical Society