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534.1 --- 534.8 --- 519.63 --- #KVIV:BB --- 519.63 Numerical methods for solution of partial differential equations --- Numerical methods for solution of partial differential equations --- 534.8 Applications of acoustics (theory) --- Applications of acoustics (theory) --- 534.1 Vibration of bodies. Excitation of vibrations. Vibratory formations with distributed mass and elasticity --- Vibration of bodies. Excitation of vibrations. Vibratory formations with distributed mass and elasticity

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This book considers recent developments in numerical error estimation and adaptive discretization for finite element and finite volume methods with particular attention given to discretization methods used frequently in computational fluid dynamics. The volume consists of six detailed articles by leading specialists covering a range of topics including a posteriori error estimation of functionals, one- and two-sided error bounds, error indicators for ad aptivity, and nd geometrical aspects of adaptive mesh refinement. This book should be of interest to readers actively working in the field as well as readers seeking a comprehensive introduction to the topic.

Finite element method. --- Fluid dynamics --- Numerical analysis. --- Mathematics. --- 519.63 --- Computer science --- Engineering --- Construction --- Industrial arts --- Technology --- Computer mathematics --- Electronic data processing --- Mathematics --- 519.63 Numerical methods for solution of partial differential equations --- Numerical methods for solution of partial differential equations --- Computer mathematics. --- Mathematical physics. --- Fluids. --- Computational intelligence. --- Computational Mathematics and Numerical Analysis. --- Theoretical, Mathematical and Computational Physics. --- Fluid- and Aerodynamics. --- Computational Intelligence. --- Intelligence, Computational --- Artificial intelligence --- Soft computing --- Hydraulics --- Mechanics --- Physics --- Hydrostatics --- Permeability --- Physical mathematics --- Mathematiques --- Mecanique des fluides

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Scientific computing is a fast growing and fast changing area whose applications to various branches of science, engineering, medicine, economics (and others) are increasing in number and relevance every day. There are two main reasons (among others) that make scientific computing change so rapidly. One is the increasing number of different research areas beginning to make use of numerical simulation: from nanotechnology to genomics, from computer­ aided diagnosis and operations in medical applications (which involve often com­ plete simulations of parts of the human body) to economics and finance. Each new application, and each new aspect of earlier applications, draws heavily on the know­ how that has been acquired on other problems with similar mathematical features. It has to be pointed out that the lofty perspective of mathematics succeeds quite often in finding connections among very different phenomena, that tum out in the end to share the same mathematical and numerical structure. In tum, new applica­ tions contribute to the cross-fertilization by "sending back" new interpretations and suggestions which are often useful in more classical applications. All this creates a resonance effect that contributes greatly to the growth rate of the whole field.

519.6 <063> --- 519.62 <063> --- 519.63 <063> --- 681.3*G17 <063> --- 681.3*G18 <063> --- 681.3*G18 <063> Partial differential equations: difference methods; elliptic equations; finite element methods; hyperbolic equations; method of lines; parabolic equations (Numerical analysis)--Congressen --- Partial differential equations: difference methods; elliptic equations; finite element methods; hyperbolic equations; method of lines; parabolic equations (Numerical analysis)--Congressen --- 681.3*G17 <063> Ordinary differential equations: boundary value problems; convergence and stability; error analysis; initial value problems; multistep methods; single step methods; stiff equations (Numerical analysis)--Congressen --- Ordinary differential equations: boundary value problems; convergence and stability; error analysis; initial value problems; multistep methods; single step methods; stiff equations (Numerical analysis)--Congressen --- 519.63 <063> Numerical methods for solution of partial differential equations--Congressen --- Numerical methods for solution of partial differential equations--Congressen --- 519.62 <063> Numerical methods for solution of ordinary differential equations--Congressen --- Numerical methods for solution of ordinary differential equations--Congressen --- 519.6 <063> Computational mathematics. Numerical analysis. Computer programming--Congressen --- Computational mathematics. Numerical analysis. Computer programming--Congressen --- Mathematical analysis. --- Analysis (Mathematics). --- Applied mathematics. --- Engineering mathematics. --- Computer mathematics. --- Analysis. --- Applications of Mathematics. --- Computational Mathematics and Numerical Analysis. --- Computer mathematics --- Electronic data processing --- Mathematics --- Engineering --- Engineering analysis --- Mathematical analysis --- 517.1 Mathematical analysis

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The second edition features lots of improvements and new material. The most significant additions include - finite difference methods and implementations for a 1D time-dependent heat equation (Chapter 1. 7. 6), - a solver for vibration of elastic structures (Chapter 5. 1. 6), - a step-by-step instruction of how to develop and test Diffpack programs for a physical application (Chapters 3. 6 and 3. 13), - construction of non-trivial grids using super elements (Chapters 3. 5. 4, 3. 6. 4, and 3. 13. 4), - additional material on local mesh refinements (Chapter 3. 7), - coupling of Diffpack with other types of software (Appendix B. 3) - high-level programming offinite difference solvers utilizing the new stencil (finite difference operator) concept in Diffpack (Appendix D. 8). Many of the examples, projects, and exercises from the first edition have been revised and improved. Some new exercises and projects have also been added. A hopefully very useful new feature is the compact overview of all the program examples in the book and the associated software files, presented in Chapter 1. 2. Errors have been corrected, many explanations have been extended, and the text has been upgraded to be compatible with Diffpack version 4. 0. The major difficulty when developing programs for numerical solution of partial differential equations is to debug and verify the implementation. This requires an interplay between understanding the mathematical model,the in­ volved numerics, and the programming tools.

Differential equations, Partial --- Numerical solutions --- Data processing. --- Diffpack (Computer file). --- 681.3 *G18 --- 519.63 --- 519.63 Numerical methods for solution of partial differential equations --- Numerical methods for solution of partial differential equations --- 681.3 *G18 Partial differential equations: difference methods; elliptic equations; finite element methods; hyperbolic equations; method of lines; parabolic equations (Numerical analysis) --- Partial differential equations: difference methods; elliptic equations; finite element methods; hyperbolic equations; method of lines; parabolic equations (Numerical analysis) --- Partial differential equations --- Numerical solutions&delete& --- Data processing --- Diffpack (Computer file) --- Computers. --- Mathematical analysis. --- Analysis (Mathematics). --- Software engineering. --- Computer mathematics. --- Computational intelligence. --- Mathematical physics. --- Theory of Computation. --- Analysis. --- Software Engineering/Programming and Operating Systems. --- Computational Mathematics and Numerical Analysis. --- Computational Intelligence. --- Theoretical, Mathematical and Computational Physics. --- Physical mathematics --- Physics --- Intelligence, Computational --- Artificial intelligence --- Soft computing --- Computer mathematics --- Electronic data processing --- Mathematics --- Computer software engineering --- Engineering --- 517.1 Mathematical analysis --- Mathematical analysis --- Automatic computers --- Automatic data processors --- Computer hardware --- Computing machines (Computers) --- Electronic brains --- Electronic calculating-machines --- Electronic computers --- Hardware, Computer --- Computer systems --- Cybernetics --- Machine theory --- Calculators --- Cyberspace