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Discrete Sobolev and Poincaré inequalities for piecewise polynomial functions. (English) Zbl 1065.65128
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.

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
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