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Compact embedding in the space of piecewise H1 functions. arXiv:1302.7079

Preprint, arXiv:1302.7079 [math.NA] (2013).
Summary: We prove a compact embedding theorem in a class of spaces of piecewise H1 functions subordinated to a class of shape regular, but not necessarily quasi-uniform triangulations of a polygonal domain. This result generalizes the Rellich–Kondrachov theorem. It is used to prove generalizations to piecewise functions of nonstandard PoincarĂ©–Friedrichs inequalities. It can be used to prove Korn inequalities for piecewise functions associated with elastic shells.

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
74S05 Finite element methods applied to problems in solid mechanics
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