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We prove a compact embedding theorem in a class of spaces of piecewise H1functions subordinated to a class of shape regular, but not necessarilyquasi-uniform triangulations of a polygonal domain. This result generalizes theRellich--Kondrachov theorem. It is used to prove generalizations to piecewisefunctions of nonstandard Poincar\'e--Friedrichs inequalities. It can be used toprove Korn inequalities for piecewise functions associated with elastic shells.

Compact embedding in the space of piecewise H1 functions