scholarly journals Finite element subspaces with optimal rates of convergence for the stationary Stokes problem

1982 ◽  
Vol 16 (1) ◽  
pp. 49-66 ◽  
Author(s):  
Lois Mansfield
Keyword(s):  
Finite Element ◽  
Stokes Problem ◽  
Rates Of Convergence ◽  
Optimal Rates Of Convergence

scholarly journals Variational eigenvalue approximation of non-coercive operators with application to mixed formulations in elasticity

SeMA Journal ◽  
2022 ◽  
Author(s):  
Salim Meddahi
Keyword(s):  
Finite Element ◽  
Mixed Finite Element ◽  
Sufficient Conditions ◽  
Rates Of Convergence ◽  
Galerkin Scheme ◽  
Eigenvalue Approximation ◽  
Finite Element Approximations ◽  
Mixed Formulations ◽  
Optimal Rates Of Convergence ◽  
Abstract Framework

AbstractWe present an abstract framework for the eigenvalue approximation of a class of non-coercive operators. We provide sufficient conditions to guarantee the spectral correctness of the Galerkin scheme and to obtain optimal rates of convergence. The theory is applied to the convergence analysis of mixed finite element approximations of the elasticity and Stokes eigensystems.

scholarly journals Local Projection Stabilization Method for Incompressible Flow Problems

2012 ◽  
Vol 17 (2) ◽  
pp. 187
Author(s):  
A.M. Essefi ◽  
K. Nafa
Keyword(s):  
Stokes Problem ◽  
Rates Of Convergence ◽  
Stabilization Method ◽  
Local Projection ◽  
Numerical Examples ◽  
Flow Problems ◽  
Local Projection Stabilization ◽  
Optimal Rates Of Convergence ◽  
Stability And Accuracy ◽  
Methods Numerical

We analyze Local Projection Stabilization (LPS) methods for the solution of Stokes problem using equal order finite elements. We investigate their convergence, stability and accuracy properties. The resulting stabilized method is shown to lead to optimal rates of convergence for both velocity and pressure approximations. We distinguish two classes of LPS methods: one-level and two-level methods. Numerical examples using bilinear interpolations are presented to validate the analysis and assess the accuracy of both approaches.  

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