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The book is suitable for advanced undergraduate and beginning graduate students of applied mathematics and engineering. The main theme is the integration of the theory of linear PDEs and the numerical solution of such equations. For each type of PDE, elliptic, parabolic, and hyperbolic, the text contains one chapter on the mathematical theory of the differential equation, followed by one chapter on finite difference methods and one on finite element methods. As preparation, the two-point boundary value problem and the initial-value problem for ODEs are discussed in separate chapters. There is also one chapter on the elliptic eigenvalue problem and eigenfunction expansion. The presentation does not presume a deep knowledge of mathematical and functional analysis. Some background on linear functional analysis and Sobolev spaces, and also on numerical linear algebra, is reviewed in two appendices.

Numerical solutions of differential equations --- Differential equations, Partial --- Equations aux dérivées partielles --- Numerical solutions --- Solutions numériques --- 519.63 --- -Partial differential equations --- Numerical methods for solution of partial differential equations --- Numerical solutions. --- -Numerical methods for solution of partial differential equations --- -519.63 Numerical methods for solution of partial differential equations --- Partial differential equations --- Equations aux dérivées partielles --- Solutions numériques --- 519.63 Numerical methods for solution of partial differential equations --- Numerical analysis --- Mathematical analysis. --- Analysis (Mathematics). --- Numerical analysis. --- Partial differential equations. --- Analysis. --- Numerical Analysis. --- Partial Differential Equations. --- Mathematical analysis --- 517.1 Mathematical analysis --- Differential equations, Partial - Numerical solutions

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Differential equations, Partial. --- Differential equations, Partial --- 517.95 --- 519.63 --- Partial differential equations --- 519.63 Numerical methods for solution of partial differential equations --- Numerical methods for solution of partial differential equations --- 517.95 Partial differential equations --- Equations aux dérivées partielles --- Monograph

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This book introduces, in an accessible way, the basic elements of Numerical PDE-Constrained Optimization, from the derivation of optimality conditions to the design of solution algorithms. Numerical optimization methods in function-spaces and their application to PDE-constrained problems are carefully presented. The developed results are illustrated with several examples, including linear and nonlinear ones. In addition, MATLAB codes, for representative problems, are included. Furthermore, recent results in the emerging field of nonsmooth numerical PDE constrained optimization are also covered. The book provides an overview on the derivation of optimality conditions and on some solution algorithms for problems involving bound constraints, state-constraints, sparse cost functionals and variational inequality constraints.

Mathematics. --- Optimization. --- Partial Differential Equations. --- Numerical Analysis. --- Differential equations, partial. --- Numerical analysis. --- Mathematical optimization. --- Mathématiques --- Analyse numérique --- Optimisation mathématique --- Mathematical models. --- Civil & Environmental Engineering --- Engineering & Applied Sciences --- Operations Research --- 519.63 --- Numerical methods for solution of partial differential equations --- 519.63 Numerical methods for solution of partial differential equations --- Differential equations, Partial. --- Constrained optimization. --- Optimization, Constrained --- Partial differential equations --- Partial differential equations. --- Mathematical optimization --- Optimization (Mathematics) --- Optimization techniques --- Optimization theory --- Systems optimization --- Mathematical analysis --- Maxima and minima --- Operations research --- Simulation methods --- System analysis

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519.63 --- 519.63 Numerical methods for solution of partial differential equations --- Numerical methods for solution of partial differential equations --- Multigrid methods (Numerical analysis) --- Partial differential equations: difference methods; elliptic equations; finite element methods; hyperbolic equations; method of lines; parabolic equations (Numerical analysis) --- Multigrid methods (Numerical analysis). --- 681.3 *G18 Partial differential equations: difference methods; elliptic equations; finite element methods; hyperbolic equations; method of lines; parabolic equations (Numerical analysis) --- 681.3 *G18 --- Numerical analysis --- Numerical solutions of differential equations

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Stochastic processes --- Artificial intelligence. Robotics. Simulation. Graphics --- Operational research. Game theory --- Image processing --- Traitement d'images --- Mathematical models --- Modèles mathématiques --- 681.3*I42 --- 519.63 --- 519.22 --- Compression (coding): approximate methods; exact coding (Image processing)--See also {681.3*E4} --- Numerical methods for solution of partial differential equations --- Statistical theory. Statistical models. Mathematical statistics in general --- 519.22 Statistical theory. Statistical models. Mathematical statistics in general --- 519.63 Numerical methods for solution of partial differential equations --- 681.3*I42 Compression (coding): approximate methods; exact coding (Image processing)--See also {681.3*E4} --- Modèles mathématiques --- Pictorial data processing --- Picture processing --- Processing, Image --- Imaging systems --- Optical data processing