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Partial Differential Equations

Modelling and Numerical Simulation

  • Book
  • © 2008

Overview

Editors:
  1. Roland Glowinski

    1. Department of Mathematics, University of Houston, USA

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    You can also search for this editor in PubMed   Google Scholar

  2. Pekka Neittaanmäki

    1. Department of Mathematical Information Technology, University of Jyväskylä, Finland

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    You can also search for this editor in PubMed   Google Scholar

  • 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

Part of the book series: Computational Methods in Applied Sciences (COMPUTMETHODS, volume 16)

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Table of contents (16 chapters)

  1. Front Matter

    Pages I-XVI
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  2. Discontinuous Galerkin and Mixed Finite Element Methods

    1. Discontinuous Galerkin Methods

      • Vivette Girault, Mary F. Wheeler
      Pages 3-26

    2. Mixed Finite Element Methods on Polyhedral Meshes for Diffusion Equations

      • Yuri A. Kuznetsov
      Pages 27-41

    3. On the Numerical Solution of the Elliptic Monge—Ampère Equation in Dimension Two: A Least-Squares Approach

      • Edward J. Dean, Roland Glowinski
      Pages 43-63

  3. Linear and Nonlinear Hyperbolic Problems

    1. Higher Order Time Stepping for Second Order Hyperbolic Problems and Optimal CFL Conditions

      • J. Charles Gilbert, Patrick Joly
      Pages 67-93

    2. Comparison of Two Explicit Time Domain Unstructured Mesh Algorithms for Computational Electromagnetics

      • Igor Sazonov, Oubay Hassan, Ken Morgan, Nigel P. Weatherill
      Pages 95-112

    3. The von Neumann Triple Point Paradox

      • Richard Sanders, Allen M. Tesdall
      Pages 113-128

  4. Domain Decomposition Methods

    1. A Lagrange Multiplier Based Domain Decomposition Method for the Solution of a Wave Problem with Discontinuous Coefficients

      • Serguei Lapin, Alexander Lapin, Jacques Périaux, Pierre-Marie Jacquart
      Pages 131-145

    2. Domain Decomposition and Electronic Structure Computations: A Promising Approach

      • Guy Bencteux, Maxime Barrault, Eric Cancès, William W. Hager, Claude Le Bris
      Pages 147-164

  5. Free Surface, Moving Boundaries and Spectral Geometry Problems

    1. Numerical Analysis of a Finite Element/Volume Penalty Method

      • Bertrand Maury
      Pages 167-185

    2. A Numerical Method for Fluid Flows with Complex Free Surfaces

      • Andrea Bonito, Alexandre Caboussat, Marco Picasso, Jacques Rappaz
      Pages 187-208

    3. Modelling and Simulating the Adhesion and Detachment of Chondrocytes in Shear Flow

      • Jian Hao, Tsorng-Whay Pan, Doreen Rosenstrauch
      Pages 209-223

    4. Computing the Eigenvalues of the Laplace-Beltrami Operator on the Surface of a Torus: A Numerical Approach

      • Roland Glowinski, Danny C. Sorensen
      Pages 225-232

  6. Inverse Problems

    1. A Fixed Domain Approach in Shape Optimization Problems with Neumann Boundary Conditions

      • Pekka Neittaanmäki, Dan Tiba
      Pages 235-244

    2. Reduced-Order Modelling of Dispersion

      • Jean-Marc Brun, Bijan Mohammadi
      Pages 245-256

  7. Finance (Option Pricing)

    1. Calibration of Lévy Processes with American Options

      • Yves Achdou
      Pages 259-277

    2. An Operator Splitting Method for Pricing American Options

      • Samuli Ikonen, Jari Toivanen
      Pages 279-292
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Keywords

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

  • Department of Mathematics, University of Houston, USA

    Roland Glowinski

  • Department of Mathematical Information Technology, University of Jyväskylä, Finland

    Pekka Neittaanmäki

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