Adaptive Finite Elements for Exterior Domain Problems

Bänsch E, Dörfler W (1998)

Publication Type: Journal article, Original article

Publication year: 1998

Journal

Numerische Mathematik Springer Verlag (Germany)

Publisher: Springer Verlag (Germany)

Book Volume: 80

Pages Range: 497-523

Journal Issue: 4

DOI: 10.1007/s002110050376

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 ℝ^d, d ∈ {2,3}. We describe a procedure to generate a sequence of bounded computational domains Ω^kh, k = 1, 2, ..., more precisely, a sequence of successively finer and larger grids, until the desired accuracy of the solution uh 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.

Authors with CRIS profile

Eberhard Bänsch Lehrstuhl für Angewandte Mathematik (Wissenschaftliches Rechnen)

Involved external institutions

Albert-Ludwigs-Universität Freiburg

Germany (DE)

How to cite

APA:

Bänsch, E., & Dörfler, W. (1998). Adaptive Finite Elements for Exterior Domain Problems. Numerische Mathematik, 80(4), 497-523. https://doi.org/10.1007/s002110050376

MLA:

Bänsch, Eberhard, and Willy Dörfler. "Adaptive Finite Elements for Exterior Domain Problems." Numerische Mathematik 80.4 (1998): 497-523.

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