Prof. Dr. Willy Dörfler /  Publikationen /  Abstract

### 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.