Convergence analysis of mixed finite element approximations to shape gradients in the Stokes equation

2019 ◽  
Vol 343 ◽  
pp. 127-150 ◽  
Author(s):  
Shengfeng Zhu ◽  
Zhiming Gao
Keyword(s):  
Finite Element ◽  
Convergence Analysis ◽  
Stokes Equation ◽  
Mixed Finite Element ◽  
Finite Element Approximations ◽  
The Stokes Equation

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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