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Adaptive FEM for Parameter-Errors in Elliptic Linear-Quadratic Parameter Estimation Problems
- Source :
- SIAM Journal on Numerical Analysis. 60:1450-1471
- Publication Year :
- 2022
- Publisher :
- Society for Industrial & Applied Mathematics (SIAM), 2022.
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Abstract
- We consider an elliptic linear-quadratic parameter estimation problem with a finite number of parameters. A novel a priori bound for the parameter error is proved and, based on this bound, an adaptive finite element method driven by an a posteriori error estimator is presented. Unlike prior results in the literature, our estimator, which is composed of standard energy error residual estimators for the state equation and suitable co-state problems, reflects the faster convergence of the parameter error compared to the (co)-state variables. We show optimal convergence rates of our method; in particular and unlike prior works, we prove that the estimator decreases with a rate that is the sum of the best approximation rates of the state and co-state variables. Experiments confirm that our method matches the convergence rate of the parameter error.
Details
- ISSN :
- 10957170 and 00361429
- Volume :
- 60
- Database :
- OpenAIRE
- Journal :
- SIAM Journal on Numerical Analysis
- Accession number :
- edsair.doi.dedup.....a8e28fe690abb41b07c3829964086f04