Brenner, Susanne C. Discrete Sobolev and Poincaré inequalities for piecewise polynomial functions. (English) Zbl 1065.65128 ETNA, Electron. Trans. Numer. Anal. 18, 42-48 (2004). Summary: 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. Cited in 13 Documents MSC: 65N30 Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs 35J25 Boundary value problems for second-order elliptic equations 26D15 Inequalities for sums, series and integrals Keywords:finite element methods; Discrete Sobolev inequality; piecewise polynomial functions; nonconforming discontinuous Galerkin methods. PDFBibTeX XMLCite \textit{S. C. Brenner}, ETNA, Electron. Trans. Numer. Anal. 18, 42--48 (2004; Zbl 1065.65128) Full Text: EuDML EMIS