```@phdthesis{Zumbusch:1995*1,
author = {G. W. Zumbusch},
title = {Simultanous h-p Adaptation in Multilevel Finite Elements},
school = {Fachbereich Mathematik und Informatik, FU Berlin},
year = {1995},
ps = {http://wissrech.ins.uni-bonn.de/research/pub/zumbusch/diss.ps.gz 1},
pdf = {http://wissrech.ins.uni-bonn.de/research/pub/zumbusch/diss.pdf 1},
urlps = {http://wissrech.ins.uni-bonn.de/research/pub/zumbusch/diss_nopic.ps.gz 1},
annote = {thesis},
type = {Dissertation},
abstract = {An important tool in engineering is the finite element
method.... The combination of both methods, the \$h\$--\$p\$
version, supplies the pre-asym\-ptotic exponentially
convergent \$p\$--version continuously with properly adapted
grids. Hence it achieves the superior exponential
convergence asymptotically, too, instead of algebraic
convergence of its ingredients the \$h\$--version and the
\$p\$--version. Although the first theoretical results
claiming these convergence rates are quite classic, the
number of codes using the \$h\$--\$p\$--version of finite
elements is still rather limited. Reasons for that are the
pure implementational complexity and the details, in
conjunction with the rumor of engineers' low precision
requirements. But the major reason is the lack of a robust
(self-) adaptive control delivering the desired exponential
convergence. ... \\ In the this thesis we present some
steps towards an efficient implementation of the
theoretically known exponential convergence. As it turns
out, an efficient implementation requires additional
theoretical considerations, which play a major role there
as well. This includes both the fully automatic
\$h\$--\$p\$--version and as a subset the \$p\$--version on
suitable grids. We present some details concerning our
approach implementing an adaptive \$h\$--\$p\$--version based
on an adaptive multilevel \$h\$--version code named {\sc