Some boundary value problems yield anisotropic solutions, e.g. solutions
with boundary layers. If such problems are to be solved with the finite
element method (FEM), anisotropically refined meshes can be
advantageous.
In order to construct these meshes or to control the error
one aims at reliable error estimators.
For \emph{isotropic} meshes many estimators are known, but they either fail
when used on \emph{anisotropic} meshes, or they were not applied yet.
For rectangular (or cuboidal) anisotropic meshes a modified
error estimator had already been found.
We are investigating error estimators on anisotropic tetrahedral or
triangular meshes because such grids offer greater geometrical flexibility.
For the Poisson equation a residual error estimator, a local Dirichlet problem
error estimator, and an $L_2$ error estimator are derived, respectively.
Additionally a residual error estimator is presented for a singularly
perturbed reaction diffusion equation.
It is important that the anisotropic mesh corresponds to the anisotropic
solution. Provided that a certain condition is satisfied, we have proven
that all estimators bound the error reliably.
| Identifer | oai:union.ndltd.org:DRESDEN/oai:qucosa.de:bsz:ch1-199801440 |
| Date | 30 October 1998 |
| Creators | Kunert, G. |
| Contributors | TU Chemnitz, SFB 393 |
| Publisher | Universitätsbibliothek Chemnitz |
| Source Sets | Hochschulschriftenserver (HSSS) der SLUB Dresden |
| Language | English |
| Detected Language | English |
| Type | doc-type:preprint |
| Format | application/pdf, application/postscript, text/plain, application/zip |
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