We consider nonconforming methods for symmetric elliptic problems and characterize their quasi-optimality in terms of suitable notions of stability and consistency. The quasi-optimality constant is determined, and the possible impact of nonconformity on its size is quantified by means of two alternative consistency measures. Identifying the structure of quasi-optimal methods, we show that their construction reduces to the choice of suitable linear operators mapping discrete functions to conforming ones. Such smoothing operators are devised in the forthcoming parts of this work for various finite element spaces.

Quasi-optimal nonconforming methods for symmetric elliptic problems. I—abstract theory / A. Veeser, P. Zanotti. - In: SIAM JOURNAL ON NUMERICAL ANALYSIS. - ISSN 0036-1429. - 56:3(2018), pp. 1621-1642.

Quasi-optimal nonconforming methods for symmetric elliptic problems. I—abstract theory

A. Veeser
Primo
;
P. Zanotti
Ultimo
2018

Abstract

We consider nonconforming methods for symmetric elliptic problems and characterize their quasi-optimality in terms of suitable notions of stability and consistency. The quasi-optimality constant is determined, and the possible impact of nonconformity on its size is quantified by means of two alternative consistency measures. Identifying the structure of quasi-optimal methods, we show that their construction reduces to the choice of suitable linear operators mapping discrete functions to conforming ones. Such smoothing operators are devised in the forthcoming parts of this work for various finite element spaces.
Consistency; Discontinuous; Nonconforming methods; Other nonconforming Galerkin methods; Quasi-optimality; Stability; Numerical Analysis
Settore MAT/08 - Analisi Numerica
2018
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/2434/594299
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