Compact embedding in the space of piecewise H1 functions
This provides a theoretical foundation for finite element analysis on irregular meshes, benefiting numerical analysts working on shell problems.
The paper proves a compact embedding theorem for piecewise H1 functions on non-uniform triangulations, generalizing the Rellich–Kondrachov theorem, and uses it to derive nonstandard Poincaré–Friedrichs and Korn inequalities.
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 Poincaré--Friedrichs inequalities. It can be used to prove Korn inequalities for piecewise functions associated with elastic shells.