Summary.
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 \({\Bbb R}^d\), \(d\in\{2,3\}\). 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. Furthermore we prove convergence of the adaptive algorithm. Numerical examples show the optimal order of convergence.
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Received July 8, 1997 /Revised version received October 23, 1997
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Bänsch, E., Dörfler, W. Adaptive finite elements for exterior domain problems. Numer. Math. 80, 497–523 (1998). https://doi.org/10.1007/s002110050376
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DOI: https://doi.org/10.1007/s002110050376