galerkin scheme
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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.

A posteriori error analysis of an enriched Galerkin method of order one for the Stokes problem

2021 ◽  
Vol 0 (0) ◽  
Author(s):  
Vivette Girault ◽  
María González ◽  
Frédéric Hecht
Keyword(s):  
Dirichlet Boundary ◽  
Stokes Problem ◽  
A Posteriori Error Estimates ◽  
Posteriori Error ◽  
A Posteriori ◽  
A Posteriori Error Analysis ◽  
Galerkin Scheme ◽  
A Posteriori Error ◽  
Hexahedral Meshes ◽  
Posteriori Error Analysis

Abstract We derive optimal reliability and efficiency of a posteriori error estimates for the steady Stokes problem, with a nonhomogeneous Dirichlet boundary condition, solved by a stable enriched Galerkin scheme (EG) of order one on triangular or quadrilateral meshes in ℝ2, and tetrahedral or hexahedral meshes in ℝ3.

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