Refined mixed finite element method for the elasticity problem in a polygonal domain

2002 ◽  
Vol 18 (3) ◽  
pp. 323-339 ◽  
Author(s):  
M. Farhloul ◽  
L. Paquet
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Mixed Finite Element ◽  
Mixed Finite Element Method ◽  
Elasticity Problem ◽  
Polygonal Domain ◽  
Element Method

scholarly journals A Refined Mixed Finite Element Method for Stationary Navier—Stokes Equations with Mixed Boundary Conditions Using Lagrange Multipliers

2007 ◽  
Vol 7 (1) ◽  
pp. 83-100
Author(s):  
S. Nicaise ◽  
L. Paquet ◽  
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Boundary Conditions ◽  
Mixed Boundary ◽  
Mixed Finite Element ◽  
Mixed Finite Element Method ◽  
Mixed Boundary Conditions ◽  
Navier Stokes ◽  
Polygonal Domain ◽  
Element Method

Abstract This paper is concerned with a dual mixed formulation of the Navier — Stokes system in a polygonal domain of the plane with mixed boundary conditions and its numerical approximation. The Neumann boundary condition is imposed using a Lagrange multiplier corresponding to the velocity field. Moreover, the strain tensor and the antisymmetric gradient tensor (vorticity), quantities of practical interest, are introduced as new unknowns. The problem is then approximated by a mixed finite element method. Quasi-optimal error estimates are finally obtained using refined meshes near singular corners.

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