Estimate of the Constant in Two Strengthened C.B.S. Inequalities for F.E.M. Systems of 2D Elasticity: Application to Multilevel Methods and a Posteriori Error Estimators

Autor:	Jean-François Maitre, Boujemâa Achchab
Rok vydání:	1996
Předmět:	Mathematical optimization Algebra and Number Theory Iterative method Applied Mathematics Estimator Finite element method Poisson's ratio symbols.namesake Quadratic equation Rate of convergence symbols Applied mathematics A priori and a posteriori Elasticity (economics) Mathematics
Zdroj:	Numerical Linear Algebra with Applications. 3:147-159
ISSN:	1099-1506 1070-5325
DOI:	10.1002/(sici)1099-1506(199603/04)3:2<147::aid-nla75>3.0.co;2-s
Popis:	The constant γ in the strengthened Cauchy-Buniakowski-Schwarz (C.B.S.) inequality plays a crucial role in the convergence rate of multilevel iterative methods as well as in the efficiency of a posteriori error estimators, that is in the framework of finite element approximations of SPD problems. We consider the approximation of the 2D elasticity problem by the Courant element. Concerning multilevel convergence rate, that is the γ corresponding to nested general triangular meshes of size h and 2h, we have proved that γ2≤ 3/4$ uniformly on the mesh and the Poisson ratio. Concerning error estimator, that is the γ corresponding to quadratic and linear approximations on the same mesh, numerical computations have shown that the exact γ for a reference element deteriorates that is goes to one, when the Poisson ratio tends to 1/2
Databáze:	OpenAIRE
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