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This book deals with the reliable verification of the accuracy of approximate solutions which is one of the central problems in modern applied analysis.After giving an overview of the methods developed for models based on partial differential equations, the author derives computable a posteriori error estimates by using methods of the theory of partial differential equations and functional analysis. These estimates are applicable to approximate solutions computed by various methods.

Differential equations, Partial. --- Error analysis (Mathematics) --- Errors, Theory of --- Instrumental variables (Statistics) --- Mathematical statistics --- Numerical analysis --- Statistics --- Partial differential equations --- A-posteriori-Abschätzung. --- Error analysis (Mathematics). --- Partielle Differentialgleichung. --- Partial Differential Equation, Approximate Solution, A Posteriori Error Estimates.

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Recent decades have seen a very rapid success in developing numerical methods based on explicit control over approximation errors. It may be said that nowadays a new direction is forming in numerical analysis, the main goal of which is to develop methods ofreliable computations. In general, a reliable numerical method must solve two basic problems: (a) generate a sequence of approximations that converges to a solution and (b) verify the accuracy of these approximations. A computer code for such a method must consist of two respective blocks: solver and checker.In this book, we are chie

Numerical analysis. --- Error-correcting codes (Information theory) --- Approximation theory. --- Theory of approximation --- Functional analysis --- Functions --- Polynomials --- Chebyshev systems --- Codes, Error-correcting (Information theory) --- Error-detecting codes (Information theory) --- Forbidden-combination check (Information theory) --- Self-checking codes (Information theory) --- Artificial intelligence --- Automatic control --- Coding theory --- Information theory --- Mathematical analysis

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This volume contains selected papers in three closely related areas: mathematical modeling in mechanics, numerical analysis, and optimization methods. The papers are based upon talks presented on the International Conference for Mathematical Modeling and Optimization in Mechanics, held in Jyväskylä, Finland, March 6-7, 2014 dedicated to Prof. N. Banichuk on the occasion of his 70th birthday. The articles are written by well-known scientists working in computational mechanics and in optimization of complicated technical models. Also, the volume contains papers discussing the historical development, the state of the art, new ideas, and open problems arising in modern continuum mechanics and applied optimization problems. Several papers are concerned with mathematical problems in numerical analysis, which are also closely related to important mechanical models. The main topics treated include: * Computer simulation methods in mechanics, physics, and biology; * Variational problems and methods; minimization algorithms; * Optimal control problems with distributed and discrete control; * Shape optimization and shape design problems in science and engineering; * Sensitivity analysis and parameters optimization of complex systems.

Civil Engineering --- Civil & Environmental Engineering --- Engineering & Applied Sciences --- Engineering design --- Mechanical engineering. --- Mathematical models. --- Engineering, Mechanical --- Engineering. --- Computer mathematics. --- Mechanics. --- Mechanics, Applied. --- Engineering design. --- Engineering Design. --- Computational Science and Engineering. --- Theoretical and Applied Mechanics. --- Design, Engineering --- Engineering --- Industrial design --- Strains and stresses --- Applied mechanics --- Engineering mathematics --- Classical mechanics --- Newtonian mechanics --- Physics --- Dynamics --- Quantum theory --- Computer mathematics --- Discrete mathematics --- Electronic data processing --- Construction --- Industrial arts --- Technology --- Design --- Mathematics --- Machinery --- Steam engineering --- Computer science. --- Mechanics, applied. --- Informatics --- Science

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This book contains the results in numerical analysis and optimization presented at the ECCOMAS thematic conference “Computational Analysis and Optimization” (CAO 2011) held in Jyväskylä, Finland, June 9–11, 2011. Both the conference and this volume are dedicated to Professor Pekka Neittaanmäki on the occasion of his sixtieth birthday. It consists of five parts that are closely related to his scientific activities and interests: Numerical Methods for Nonlinear Problems; Reliable Methods for Computer Simulation; Analysis of Noised and Uncertain Data; Optimization Methods; Mathematical Models Generated by Modern Technological Problems. The book also includes a short biography of Professor Neittaanmäki.

Mathematics --- Mathematical physics --- Classical mechanics. Field theory --- Applied physical engineering --- Computer science --- Computer. Automation --- theoretische fysica --- toegepaste mechanica --- informatica --- externe fixatie (geneeskunde --- wiskunde --- ingenieurswetenschappen --- mechanica

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This volume contains selected papers in three closely related areas: mathematical modeling in mechanics, numerical analysis, and optimization methods. The papers are based upon talks presented  on the International Conference for Mathematical Modeling and Optimization in Mechanics, held in Jyväskylä, Finland, March 6-7, 2014 dedicated to Prof. N. Banichuk on the occasion of his 70th birthday. The articles are written by well-known scientists working in computational mechanics and in optimization of complicated technical models. Also, the volume contains papers discussing the historical development, the state of the art, new ideas, and open problems arising in  modern continuum mechanics and applied optimization problems. Several papers are concerned with mathematical problems in numerical analysis, which are also closely related to important mechanical models. The main topics treated include:  * Computer simulation methods in mechanics, physics, and biology;  * Variational problems and methods; minimization algorithms;  * Optimal control problems with distributed and discrete control;  * Shape optimization and shape design problems in science and engineering;  * Sensitivity analysis and parameters optimization of complex systems.

Mathematics --- Classical mechanics. Field theory --- Materials sciences --- Applied physical engineering --- Production management --- Computer science --- Computer. Automation --- DFMA (design for manufacture and assembly) --- toegepaste mechanica --- computers --- informatica --- informaticaonderzoek --- ingenieurswetenschappen --- mechanica