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Adaptive Finite Element Methods for Parameter Identification Problems

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Model Based Parameter Estimation

Part of the book series: Contributions in Mathematical and Computational Sciences ((CMCS,volume 4))

Abstract

This chapter provides an overview on the use of adaptive finite element methods for parameter identification problems governed by partial differential equations. We discuss a posteriori error estimates for the finite element discretization error with respect to a given quantity of interest for both stationary (elliptic) and nonstationary (parabolic) problems. These error estimates guide adaptive algorithms for mesh refinement, which are tailored to the parameter identification problem. The capability of the presented methods is demonstrated on two model examples of (stationary and nonstationary) combustion problems. Moreover we present a recently developed technique for efficient computation of the Tikhonov regularization parameter in the context of distributed parameter estimation using adaptive finite element methods.

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Authors and Affiliations

  1. Lehrstuhl für Mathematische Optimierung, Technische Universität München, Fakultät für Mathematik, Boltzmannstraße 3, 85748, Garching b. München, Germany

    Boris Vexler

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  1. Boris Vexler
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Correspondence to Boris Vexler .

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Editors and Affiliations

  1. Interdisciplinary Center for Scientific, Computing (IWR), Heidelberg University, Im Neuenheimer Feld 368, Heidelberg, 69120, Germany

    Hans Georg Bock

  2. Institute for Applied Mathematics, Heidelberg University, Im Neuenheimer Feld 294, Heidelberg, 69120, Germany

    Thomas Carraro

  3. Interdisciplinary Center for Scientific, Computing (IWR), Heidelberg University, Im Neuenheimer Feld 368, Heidelberg, 69120, Germany

    Willi Jäger

  4. Interdisciplinary Center for, Scientific Computing (IWR), Heidelberg University, Im Neuenheimer Feld 368, Heidelberg, 69120, Germany

    Stefan Körkel

  5. Institute for Applied Mathematics, Heidelberg University, Im Neuenheimer Feld 293, Heidelberg, 69120, Germany

    Rolf Rannacher

  6. Interdisciplinary Center for Scientific, Computing (IWR), Heidelberg University, Im Neuenheimer Feld 368, Heidelberg, 69120, Germany

    Johannes P. Schlöder

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Vexler, B. (2013). Adaptive Finite Element Methods for Parameter Identification Problems. In: Bock, H., Carraro, T., Jäger, W., Körkel, S., Rannacher, R., Schlöder, J. (eds) Model Based Parameter Estimation. Contributions in Mathematical and Computational Sciences, vol 4. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-30367-8_2

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