Volume 18, pp. 42-48, 2004.

Discrete Sobolev and Poincaré inequalities for piecewise polynomial functions

Susanne C. Brenner

Abstract

Discrete Sobolev and Poincaré inequalities are derived for piecewise polynomial functions on two dimensional domains. These inequalities can be applied to classical nonconforming finite element methods and discontinuous Galerkin methods.

Full Text (PDF) [108 KB]

Key words

discrete Sobolev inequality, discrete Poincaré inequality, piecewise polynomial functions, nonconforming, discontinuous Galerkin.

AMS subject classifications

65N30.

ETNA articles which cite this article

Vol. 30 (2008), pp. 107-127 Susanne C. Brenner, Luke Owens, and Li-Yeng Sung: A weakly over-penalized symmetric interior penalty method
Vol. 41 (2014), pp. 262-288 Michael Neilan: A unified analysis of three finite element methods for the Monge-Ampère equation

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