For the inf-sup condition on mesh-dependent norms on a nonconvex polygon

Abstract

It is shown that the inf-sup condition, called the Babuska-Brezzi condition, is valid for certain mesh-dependent norms on a nonconvex polygonal domain. A bilinear form that is derived by inserting the corner singularity expansion into the Laplace equation is considered. A mesh-dependent fractional norm related to the least order of the corner singularity at a concave vertex is considered. (C) 2007 Wiley Periodicals, Inc.