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An adaptive strategy for elliptic problems including
a posteriori controlled boundary approximation
W Dörfler & M Rumpf
Institut of Applied Mathematics,
University of Freiburg
Hermann-Herder-Str. 10,
79104 Freiburg,
Germany
Abstract
We derive a posteriori error estimates for
the approximation of linear elliptic problems
on domains with piecewise smooth boundary. The numerical solution
is assumed to be defined
on a Finite Element mesh, whose boundary vertices are located on
the boundary of the continuous problem.
No assumption is made on a geometrical fitting shape.
A strategy is given to compute
the effect of the non-discretized part of the domain on the error
starting from a coarse mesh.
This includes the use of a stable path following strategy,
which supplies a sufficient geometrical approximation of the
domain boundary.
Based on a posteriori estimates, the discretization
will be, if necessary, enlarged and refined
using Delaunay techniques.
Numerical examples illustrate that errors outside the initial
discretization will be detected.
This would especially imply that parts of the domain, where the measured
error is small, stay non-discretized.
Last modified Fri Jun 21 19:19:12 GB-Eire 1996
(DBD)