Jan Chleboun's Books

Uncertain Input Data Problems and the Worst Scenario Method

By: Ivan Hlavacek,Jan Chleboun,Ivo Babuska

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Uncertain Input Data Problems and the Worst Scenario Method

By: Ivan Hlavacek,Jan Chleboun,Ivo Babuska

This book deals with the impact of uncertainty in input data on the outputs of mathematical models. Uncertain inputs as scalars, tensors, functions, or domain boundaries are considered. In practical terms, material parameters or constitutive laws, for instance, are uncertain, and quantities as local temperature, local mechanical stress, or local displacement are monitored. The goal of the worst scenario method is to extremize the quantity over the set of uncertain input data.A general mathematical scheme of the worst scenario method, including approximation by finite element methods, is presented, and then applied to various state problems modeled by differential equations or variational inequalities: nonlinear heat flow, Timoshenko beam vibration and buckling, plate buckling, contact problems in elasticity and thermoelasticity with and without friction, and various models of plastic deformation, to list some of the topics. Dozens of examples, figures, and tables are included.Although the book concentrates on the mathematical aspects of the subject, a substantial part is written in an accessible style and is devoted to various facets of uncertainty in modeling and to the state of the art techniques proposed to deal with uncertain input data.A chapter on sensitivity analysis and on functional and convex analysis is included for the reader's convenience.·Rigorous theory is established for the treatment of uncertainty in modeling· Uncertainty is considered in complex models based on partial differential equations or variational inequalities · Applications to nonlinear and linear problems with uncertain data are presented in detail: quasilinear steady heat flow, buckling of beams and plates, vibration of beams, frictional contact of bodies, several models of plastic deformation, and more ·Although emphasis is put on theoretical analysis and approximation techniques, numerical examples are also present·Main ideas and approaches used today to handle uncertainties in modeling are described in an accessible form·Fairly self-contained book

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485

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Elsevier

Published Date

ISBN 10

0080543375

ISBN 13

9780080543376

Simplicial Partitions with Applications to the Finite Element Method

By: Jan Brandts,Sergey Korotov,Michal Křížek

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Simplicial Partitions with Applications to the Finite Element Method

By: Jan Brandts,Sergey Korotov,Michal Křížek

This monograph focuses on the mathematical and numerical analysis of simplicial partitions and the finite element method. This active area of research has become an essential part of physics and engineering, for example in the study of problems involving heat conduction, linear elasticity, semiconductors, Maxwell's equations, Einstein's equations and magnetic and gravitational fields. These problems require the simulation of various phenomena and physical fields over complicated structures in three (and higher) dimensions. Since not all structures can be decomposed into simpler objects like d-dimensional rectangular blocks, simplicial partitions are important. In this book an emphasis is placed on angle conditions guaranteeing the convergence of the finite element method for elliptic PDEs with given boundary conditions. It is aimed at a general mathematical audience who is assumed to be familiar with only a few basic results from linear algebra, geometry, and mathematical and numerical analysis.

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Page Count

197

Publisher

Springer Nature

Published Date

ISBN 10

3030556778

ISBN 13

9783030556778

Uncertain Input Data Problems and the Worst Scenario Method

By: Ivan Hlavacek,Jan Chleboun,Ivo Babuska

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Uncertain Input Data Problems and the Worst Scenario Method

By: Ivan Hlavacek,Jan Chleboun,Ivo Babuska

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N/A

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Solve jigsaw puzzle

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Page Count

485

Publisher

Elsevier

Published Date

ISBN 10

0080543375

ISBN 13

9780080543376

Book's by Jan Chleboun

Uncertain Input Data Problems and the Worst Scenario Method

Uncertain Input Data Problems and the Worst Scenario Method

Simplicial Partitions with Applications to the Finite Element Method

Simplicial Partitions with Applications to the Finite Element Method

Uncertain Input Data Problems and the Worst Scenario Method

Uncertain Input Data Problems and the Worst Scenario Method

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