Convergence of Adaptive Edge Element Methods for the 3D Eddy Currents Equations
R.H.W. Hoppe 1, J. Schoberl 21 Institut fur Mathematik, Universitat Augsburg, D-86159, Augsburg, Germany, and Department of Mathematics, University of Houston, Houston, TX 77204-3008, USA
2 Dept. for Mathematics CCES (Center for Computational Engineering Science), RWTH Aachen, D-52074 Aachen, Germany
Received 2007-10-25 Revised 2008-7-7 Accepted 2009-2-5 Online 2009-4-27
We consider an Adaptive Edge Finite Element Method (AEFEM) for the 3D eddy currents equations with variable coefficients using a residual-type a posteriori error estimator. Both the components of the estimator and certain oscillation terms, due to the occurrence of the variable coefficients, have to be controlled properly within the adaptive loop which is taken care of by appropriate bulk criteria. Convergence of the AEFEM in terms of reductions of the energy norm of the discretization error and of the oscillations is shown. Numerical results are given to illustrate the performance of the AEFEM.
Key words: Adaptive edge elements, 3D eddy currents equations, Convergence analysis, Error and oscillation reduction, Residual type a posteriori error estimates.
AMS subject classifications: 65F10, 65N30.
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