Abstract
We consider automatic mesh refinement for parameter identification problems involving PDEs. The state equation is discretized by the finite element method on locally refined meshes. The idea is to solve the inverse problem on a cheap discrete model which still captures the “essential” features of the physical problem under consideration. To this end, we derive an a posteriori error estimator for the error with respect to the unknown parameter. The estimator is used to successively improve the accuracy by appropriate mesh refinement. In addition, it gives the possibility of quantitative error control. Numerical results demonstrate the performance of the method.
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Becker, R., Vexler, B. (2003). Mesh Adaptation for Parameter Identification Problems. In: Desch, W., Kappel, F., Kunisch, K. (eds) Control and Estimation of Distributed Parameter Systems. ISNM International Series of Numerical Mathematics, vol 143. Birkhäuser, Basel. https://doi.org/10.1007/978-3-0348-8001-5_3
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DOI: https://doi.org/10.1007/978-3-0348-8001-5_3
Publisher Name: Birkhäuser, Basel
Print ISBN: 978-3-0348-9399-2
Online ISBN: 978-3-0348-8001-5
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