Adaptive finite elements for exterior domain problems |
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Authors: | E Bänsch W Dörfler |
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Institution: | Zentrum für Technomathematik, FB 3, Universit?t Bremen, D-28334 Bremen; e-mail: baensch@math.uni-bremen.de, DE Institut für Angewandte Mathematik, Universit?t Freiburg, Hermann-Herder-Str. 10, D-79104 Freiburg; e-mail: willy@mathematik.uni-freiburg.de, DE
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Abstract: | 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 , . We describe a procedure to generate a sequence of bounded computational domains , , more precisely, a sequence of successively finer and larger grids, until the desired accuracy of the solution 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.
Received July 8, 1997 /Revised version received October 23, 1997 |
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Keywords: | Mathematics Subject Classification (1991):65N15 65N30 65N50 |
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