Quasi-optimal nonconforming methods for symmetric elliptic problems. I\n -- Abstract theory

2017/10/09 by Andreas Veeser, Veeser, Andreas, Pietro Zanotti +1
Engineering · Computer Science · #Advanced Numerical Methods in Computational Mathematics #Advanced Mathematical Modeling in Engineering #Contact Mechanics and Variational Inequalities

paper · pdf · doi:10.48550/arxiv.1710.03331

Abstract

We consider nonconforming methods for symmetric elliptic problems and\ncharacterize their quasi-optimality in terms of suitable notions of stability\nand consistency. The quasi-optimality constant is determined and the possible\nimpact of nonconformity on its size is quantified by means of two alternative\nconsistency measures. Identifying the structure of quasi-optimal methods, we\nshow that their construction reduces to the choice of suitable linear operators\nmapping discrete functions to conforming ones. Such smoothing operators are\ndevised in the forthcoming parts of this work for various finite element\nspaces.\n

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