Circumventing the Babuška-Brezzi condition in mixed finite element approximations of elliptic variational inequalities

1992 ◽  
Vol 97 (2) ◽  
pp. 193-210 ◽  
Author(s):  
Helio J.C. Barbosa ◽  
Thomas J.R. Hughes
Keyword(s):  
Finite Element ◽  
Variational Inequalities ◽  
Mixed Finite Element ◽  
Finite Element Approximations ◽  
Elliptic Variational Inequalities

New Mixed Finite Element Formulations for Transient and Steady State Creep Problems

1989 ◽  
Vol 42 (11S) ◽  
pp. S150-S156
Author(s):  
Abimael F. D. Loula ◽  
Joa˜o Nisan C. Guerreiro
Keyword(s):  
Finite Element ◽  
Steady State ◽  
Mixed Finite Element ◽  
Finite Element Approximation ◽  
Steady State Creep ◽  
Element Approximation ◽  
New Approach ◽  
Finite Element Approximations ◽  
Transient Problems ◽  
Transient And Steady State

We apply the mixed Petrov–Galerkin formulation to construct finite element approximations for transient and steady-state creep problems. With the new approach we recover stability, convergence, and accuracy of some Galerkin unstable approximations. We also present the main results on the numerical analysis and error estimates of the proposed finite element approximation for the steady problem, and discuss the asymptotic behavior of the continuum and discrete transient problems.

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