Basic Principles Of Feedback And Adaptive Approaches In The Finite Element Method
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The Finite Element Method and Its Reliability
The finite element method is a numerical method widely used in engineering. Experience shows that unreliable computation can lead to very serious consequences. Hence reliability questions stand more and more at the forefront of engineering and theoretical interests. The present book presents the mathematical theory of the finite element method and focuses on the question of how reliable computed results really are. It addresses among other topics the local behaviour, errors caused by pollution, superconvergence, and optimal meshes. Many computational examples illustrate the importance of the theoretical conclusions for practical computations. Graduate students, lecturers, and researchers in mathematics, engineering, and scientific computation will benefit from the clear structure of the book, and will find this a very useful reference.
Finite Element Analysis
Covers the fundamentals of linear theory of finite elements, from both mathematical and physical points of view. Major focus is on error estimation and adaptive methods used to increase the reliability of results. Incorporates recent advances not covered by other books.
Basic Principles of Feedback and Adaptive Approaches in the Finite Element Method
The notion of feedback and adaptivity in numerical computations has attracted great attention in the recent years. All the modern ODE's solvers for initial value problems and quadratures are feedback methods. The feedback methods are increasingly in the focus of interest in the area of numerical solution of PDE and computational mechanics. Many reports, preprints and papers dealing with the adaptivity appeared recently. It seems to be that successful computation of today's large complex problems cannot be made without some kind of feedback or adaptive approach. This paper addresses the basic notions of the theory of feedback and adaptive finite element methods. An illustrative example of the finite element method for solving nonlinear differential equation of the elliptic type is presented. Numerical example of regridding process is given.