Adaptive finite elements for exterior domain problems.
E. Bänsch,
W. Dörfler
Abstract:
We present an adaptive finite element method for solving
elliptic problems in exterior domains, that is for problems
in the exterior of a bounded closed domain in $\rz^d$,
$d\in\{2,3\}$.
We describe a procedure to generate a sequence of bounded
computational domains $\Omega_h^k$, $k=1,2,...$, more precisely,
a sequence of successively finer and larger grids, until
the desired accuracy of the solution $u_h$ is reached.
To this end we prove an a posteriori error estimate for the
error on the unbounded domain in the energy norm by means
of a residual based error estimator.
Numerical examples show the optimal order of convergence.
AMS-Classification: 65N15, 65N30, 65N50.
Keywords: Adaptive mesh refinement, a posteriori error
estimate, Poisson's equation, exterior domains.
Appeared in: Numer. Math. 80 (1998), 497-523.
