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Adaptive Finite Element Methods for Parameter Identification Problems

  • Boris Vexler
Chapter
Part of the Contributions in Mathematical and Computational Sciences book series (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.

Keywords

Optimal Control Problem Error Estimator Posteriori Error Discretization Error Posteriori Error Estimate 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer-Verlag Berlin Heidelberg 2013

Authors and Affiliations

  1. 1.Lehrstuhl für Mathematische Optimierung, Technische Universität MünchenFakultät für MathematikGarching b. MünchenGermany

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