Research Group of Prof. Dr. M. Griebel
Institute for Numerical Simulation

  author = {G. W. Zumbusch},
  title = {Simultanous h-p Adaptation in Multilevel Finite Elements},
  school = {Fachbereich Mathematik und Informatik, FU Berlin},
  year = {1995},
  ps = { 1},
  pdf = { 1},
  urlps = { 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
		  Kaskade}. This software package uses unstructured grids of
		  triangles in two dimensions and tetrahedra in three