D. Leykekhman, Pointwise localized error estimates for parabolic finite element equations, Numer. Math. 96 (2003), no. 3, 583--600.  (ps),(pdf)


abstract:

We derive pointwise weighted error estimates for a semidiscrete
finite element method applied to parabolic equations.
The results extend those obtained by A.H. Schatz for stationary
elliptic problems. In particular,they show that the error is more
localized for higher order elements.

C. Hruska, D. Leykekhman, D. Pinzon, B. Shay, J. Foisy, The shortest enclosure of two connected regions in a corner, Rocky Mountain Journal of Mathematics 31 (2001), no. 2, 437--482.

abstract:

Fix a sector in the Euclidean plane bounded by two rays emanating
from a common point. We investigate arc-length minimizing enclosures
of two connected regions in thissector with prescribed areas, where
the bounding rays do not contribute to the arc-length. We show that
the perimeter minimizing configuration is one of two possible types:
two concentric circular arcs, or a truncated standard double bubble.