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Poincaré–Friedrichs inequalities for piecewise $$H^{1}$$ functions. (English) Zbl 1045.65100
Poincaré-Friedrichs inequalities are established on polyhedral domains $$\Omega$$ for piecewise $$H^{1}$$ functions with respect to a partition by open polygons or polyhedra. The inequalities involve the jumps of the functions across the sides of the subdomains. They can be applied to classical nonconforming finite element methods, mortar methods, and discontinuous Galerkin methods.

##### MSC:
 65N30 Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs 46E35 Sobolev spaces and other spaces of “smooth” functions, embedding theorems, trace theorems 65N55 Multigrid methods; domain decomposition for boundary value problems involving PDEs
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