Wenbin Liu

Ningning Yan

Summary: "This book emphasizes the discussions of some unique issues from the adaptive finite element approximation of optimal control. The main idea used in the approximation error analysis (both a priori and a posteriori) is to first combine convex analysis and interpolation error estimations of suitable interpolators, which much depend on the structure of the control constraints, to derive the error estimates for the control via the variational inequalities in the optimality conditions, and then to apply the standard techniques to derive the error estimates for the state equations. The need, the framework and the techniques of using multi adaptive meshes in developing efficient numerical algorithms for optimal control have been emphasized throughout the book. The book starts from several typical examples of optimal control problems and then discusses existence and optimality conditions for some optimal control problems. It is believed that these discussions are especially useful for the researchers and students who first entered this area. Then the finite element approximation schemes for several typical optimal control problems are set up, their a priori and a posteriori error estimates are derived following the main idea mentioned, and their computational methods are studied."-- Publisher website, viewed 13th July, 2012.

Optimal Control Governed by PDEs

Adaptive Finite Element Methods

Fei Han

Henry Han

Tie Wei

This book constitutes selected papers of the Third International Conference on Data Science, Medicine and Bioinformatics, IDMB 2019, held in Nanning, China, in June 2019. The 19 full papers and 1 short paper were carefully reviewed and selected from 93 submissions. The papers are organized according to the following topical sections: business data science: fintech, management, and analytics.- health and biological data science.- novel data science theory and applications.

Wenbin Liu

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