The Adaptive Finite Element Technique and Its Synthesis with the Approximately Globally Convergent Numerical Method

Larisa Beilina and Michael Victor Klibanov
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Larisa Beilina: Chalmers University of Technology Gothenburg University, Department of Mathematical Sciences
Michael Victor Klibanov: University of North Carolina

Chapter Chapter 4 in Approximate Global Convergence and Adaptivity for Coefficient Inverse Problems, 2012, pp 193-293 from Springer

Abstract: Abstract In Chap. 2, we have described our approximately globally convergent numerical method for a CIP for the hyperbolic $$ c\,(x)\,{u_{tt}}=\triangle u.$$ We remind that the notion of the approximate global convergence was introduced in Definition 1.1.2.1. This method addresses the first central question of this book posed in the beginning of the introductory Chap. 1: Given a CIP, how to obtain a good approximation for the exact solution without an advanced knowledge of a small neighborhood of this solution? Theorems 2.8.2 and 2.9.4 guarantee that, within the frameworks of the first and the second approximate mathematical models respectively (Sects. 2.8.4 and 2.9.2), this approximation is obtained indeed for our CIP.

Keywords: Inverse Problem; Global Convergence; Posteriori Error; Posteriori Error Estimate; Forward Problem (search for similar items in EconPapers)
Date: 2012
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DOI: 10.1007/978-1-4419-7805-9_4

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