The Dual Mixed Finite Element Method for the Heat Diffusion Equation in a Polygonal Domain, I

2007 ◽  
pp. 239-256 ◽  
Author(s):  
Mohamed Farhloul ◽  
Réda Korikache ◽  
Luc Paquet
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Diffusion Equation ◽  
Mixed Finite Element ◽  
Mixed Finite Element Method ◽  
Heat Diffusion ◽  
Polygonal Domain ◽  
Heat Diffusion Equation ◽  
Domain I ◽  
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.

Analysis of an augmented fully-mixed finite element method for a bioconvective flows model

2021 ◽  
Vol 393 ◽  
pp. 113504
Author(s):  
Eligio Colmenares ◽  
Gabriel N. Gatica ◽  
Willian Miranda
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Mixed Finite Element ◽  
Mixed Finite Element Method ◽  
Element Method
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