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Differential equations, Elliptic --- Differential equations, Parabolic --- Galerkin methods. --- Numerical solutions. --- 519.63 --- Numerical methods for solution of partial differential equations --- 519.63 Numerical methods for solution of partial differential equations --- Galerkin methods --- Sinc-Galerkin methods --- Sinc methods --- Numerical analysis --- Numerical solutions

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Spectral theory (Mathematics) --- Finite difference methods --- Spectre (Mathématiques) --- Finite differences --- 519.63 --- 519.63 Numerical methods for solution of partial differential equations --- Numerical methods for solution of partial differential equations --- Functional analysis --- Hilbert space --- Measure theory --- Transformations (Mathematics) --- Differences, Finite --- Finite difference method --- Numerical analysis --- Finite differences. --- Spectral theory (Mathematics).

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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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Fluid dynamics --- 519.6 --- 519.63 --- 681.3*G18 --- Computational mathematics. Numerical analysis. Computer programming --- Numerical methods for solution of partial differential equations --- Partitial differential equations: domain decomposition methods; elliptic equations; finite difference methods; finite element methods; finite volume methods; hyperbolic equations; inverse problems; iterative solution techniques; methods of lines; multigrid and multilevel methods; parabolic equations; special methods --- 519.63 Numerical methods for solution of partial differential equations --- 519.6 Computational mathematics. Numerical analysis. Computer programming --- Engineering mathematics --- Congresses. --- Calculs numériques

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Spectral methods are well-suited to solve problems modeled by time-dependent partial differential equations: they are fast, efficient and accurate and widely used by mathematicians and practitioners. This class-tested 2007 introduction, the first on the subject, is ideal for graduate courses, or self-study. The authors describe the basic theory of spectral methods, allowing the reader to understand the techniques through numerous examples as well as more rigorous developments. They provide a detailed treatment of methods based on Fourier expansions and orthogonal polynomials (including discussions of stability, boundary conditions, filtering, and the extension from the linear to the nonlinear situation). Computational solution techniques for integration in time are dealt with by Runge-Kutta type methods. Several chapters are devoted to material not previously covered in book form, including stability theory for polynomial methods, techniques for problems with discontinuous solutions, round-off errors and the formulation of spectral methods on general grids. These will be especially helpful for practitioners.

519.63 --- 519.6 --- 517.95 --- Numerical methods for solution of partial differential equations --- Computational mathematics. Numerical analysis. Computer programming --- Partial differential equations --- Differential equations, Hyperbolic. --- Differential equations, Partial. --- Spectral theory (Mathematics) --- Spectral theory (Mathematics). --- 517.95 Partial differential equations --- 519.6 Computational mathematics. Numerical analysis. Computer programming --- 519.63 Numerical methods for solution of partial differential equations --- Differential equations, Hyperbolic --- Differential equations, Partial --- Functional analysis --- Hilbert space --- Measure theory --- Transformations (Mathematics) --- Hyperbolic differential equations