On the numerical analysis of some variational problems with nonhomogeneous boundary conditions (Q1275842)

This paper introduces a new technique to get energy estimates for non-convex problems, with nonlinear boundary conditions in terms of the mesh size in a finite elements scheme. A possible physical setting for the problem is a function \(\phi:\mathbb{R}^n\to \mathbb{R}\) which may be interpreted as a stored energy density that vanishes at various points in \(\mathbb{R}^n\). The essential theorems are given in Section 2 of the paper, where error bounds of the form \(Ch^p\) are obtained where \(p=1/2\), \(q/(1+ 1)\) or \(r/(r+1)\) and where \(C\) is independent of \(h\). Here, \(q>0\) is specified in the problem and \(r\) is the infimum of \(q\) and \(1\).