English

Compact embedding in the space of piecewise H1 functions

Numerical Analysis 2013-03-01 v1

Abstract

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 Poincar\'e--Friedrichs inequalities. It can be used to prove Korn inequalities for piecewise functions associated with elastic shells.

Keywords

Cite

@article{arxiv.1302.7079,
  title  = {Compact embedding in the space of piecewise H1 functions},
  author = {Sheng Zhang},
  journal= {arXiv preprint arXiv:1302.7079},
  year   = {2013}
}
R2 v1 2026-06-21T23:34:08.945Z