Overview
- Editors:
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Roland Glowinski
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Department of Mathematics, University of Houston, USA
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Pekka Neittaanmäki
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Department of Mathematical Information Technology, University of Jyväskylä, Finland
- Covers a wides spectrum of topics related to the numerical solution of partial differential equations
- Serves as state-of-the-art reference for the scientist or practitioner solving problems in science of engineering described by partial differential equations
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Table of contents (16 chapters)
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Discontinuous Galerkin and Mixed Finite Element Methods
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- Vivette Girault, Mary F. Wheeler
Pages 3-26
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- Edward J. Dean, Roland Glowinski
Pages 43-63
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Linear and Nonlinear Hyperbolic Problems
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- J. Charles Gilbert, Patrick Joly
Pages 67-93
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- Igor Sazonov, Oubay Hassan, Ken Morgan, Nigel P. Weatherill
Pages 95-112
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- Richard Sanders, Allen M. Tesdall
Pages 113-128
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Domain Decomposition Methods
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- Serguei Lapin, Alexander Lapin, Jacques Périaux, Pierre-Marie Jacquart
Pages 131-145
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- Guy Bencteux, Maxime Barrault, Eric Cancès, William W. Hager, Claude Le Bris
Pages 147-164
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Free Surface, Moving Boundaries and Spectral Geometry Problems
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- Andrea Bonito, Alexandre Caboussat, Marco Picasso, Jacques Rappaz
Pages 187-208
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- Jian Hao, Tsorng-Whay Pan, Doreen Rosenstrauch
Pages 209-223
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- Roland Glowinski, Danny C. Sorensen
Pages 225-232
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Inverse Problems
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- Pekka Neittaanmäki, Dan Tiba
Pages 235-244
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- Jean-Marc Brun, Bijan Mohammadi
Pages 245-256
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Finance (Option Pricing)
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- Samuli Ikonen, Jari Toivanen
Pages 279-292
About this book
For more than 250 years partial di?erential equations have been clearly the most important tool available to mankind in order to understand a large variety of phenomena, natural at ?rst and then those originating from - man activity and technological development. Mechanics, physics and their engineering applications were the ?rst to bene?t from the impact of partial di?erential equations on modeling and design, but a little less than a century ago the Schr¨ odinger equation was the key opening the door to the application of partial di?erential equations to quantum chemistry, for small atomic and molecular systems at ?rst, but then for systems of fast growing complexity. The place of partial di?erential equations in mathematics is a very particular one: initially, the partial di?erential equations modeling natural phenomena were derived by combining calculus with physical reasoning in order to - press conservation laws and principles in partial di?erential equation form, leading to the wave equation, the heat equation, the equations of elasticity, the Euler and Navier–Stokes equations for ?uids, the Maxwell equations of electro-magnetics, etc. It is in order to solve ‘constructively’ the heat equation that Fourier developed the series bearing his name in the early 19th century; Fourier series (and later integrals) have played (and still play) a fundamental roleinbothpureandappliedmathematics,includingmanyareasquiteremote from partial di?erential equations. On the other hand, several areas of mathematics such as di?erential ge- etry have bene?ted from their interactions with partial di?erential equations.
Editors and Affiliations
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Department of Mathematics, University of Houston, USA
Roland Glowinski
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Department of Mathematical Information Technology, University of Jyväskylä, Finland
Pekka Neittaanmäki