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Compatible Spatial Discretizations

  • Conference proceedings
  • © 2006

Overview

Editors:
  1. Douglas N. Arnold

    1. Institute for Mathematics and its Applications, University of Minnesota, Minneapolis, USA

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  2. Pavel B. Bochev

    1. Computational Mathematics and Algorithms Department, Sandia National Laboratories, Alburquerque, USA

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  3. Richard B. Lehoucq

    1. Computational Mathematics and Algorithms Department, Sandia National Laboratories, Alburquerque, USA

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  4. Roy A. Nicolaides

    1. Department of Mathematical Sciences, Carnegie Mellon University, Pittsburgh, USA

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  5. Mikhail Shashkov

    1. Theoretical Division, Los Alamos National Laboratory, Los Alamos, USA

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  • Original contributions by researchers with a common interest in the problems, but with diverse mathematical expertise and perspective
  • Abstracts and presentation slides from the workshop can be accessed on the internet

Part of the book series: The IMA Volumes in Mathematics and its Applications (IMA, volume 142)

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Table of contents (11 papers)

  1. Front Matter

    Pages i-xiv
    Download chapter PDF

  2. Numerical Convergence of the MPFA O-Method for General Quadrilateral Grids in Two and Three Dimensions

    • Ivar Aavatsmark, Geir Terje Eigestad, Runhild Aae Klausen
    Pages 1-21

  3. Differential Complexes and Stability of Finite Element Methods I. The de Rham Complex

    • Douglas N. Arnold, Richard S. Falk, Ragnar Winther
    Pages 23-46

  4. Defferential Complexes and Stability of Finite Element Methods II: The Elasticity Complex

    • Douglas N. Arnold, Richard S. Falk, Ragnar Winther
    Pages 47-67

  5. On the Role of Involutions in the Discontinuous Galerkin Discretization of Maxwell and Magnetohydrodynamic Systems

    • Timothy Barth
    Pages 69-88

  6. Principles of Mimetic Discretizations of Differential Operators

    • Pavel B. Bochev, James M. Hyman
    Pages 89-119

  7. Compatible Discretizations for Eigenvalue Problems

    • Daniele Boffi
    Pages 121-142

  8. Conjugated Bubnov-Galerkin Infinite Element for Maxwell Equations

    • L. Demkowicz, J. Kurtz
    Pages 143-159

  9. Covolume Discretization of Differential Forms

    • R. A. Nicolaides, K. A. Trapp
    Pages 161-171

  10. Mimetic Reconstruction of Vectors

    • J. Blair Perot, Dragan Vidovic, Pieter Wesseling
    Pages 173-188

  11. A Cell-Centered Finite Difference Method on Quadrilaterals

    • Mary F. Wheeler, Ivan Yotov
    Pages 189-207

  12. Development and Application of Compatible Discretizations of Maxwell’s Equations

    • Daniel A. White, Joseph M. Koning, Robert N. Rieben
    Pages 209-234

  13. Back Matter

    Pages 235-247
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Keywords

About this book

The IMA Hot Topics workshop on compatible spatialdiscretizations was held May 11-15, 2004 at the University of Minnesota. The purpose of the workshop was to bring together scientists at the forefront of the research in the numerical solution of PDEs to discuss recent advances and novel applications of geometrical and homological approaches to discretization. This volume contains original contributions based on the material presented at the workshop. A unique feature of the collection is the inclusion of work that is representative of the recent developments in compatible discretizations across a wide spectrum of disciplines in computational science.

Compatible spatial discretizations are those that inherit or mimic fundamental properties of the PDE such as topology, conservation, symmetries, and positivity structures and maximum principles. The papers in the volume offer a snapshot of the current trends and developments in compatible spatial discretizations. The reader will find valuable insights on spatial compatibility from several different perspectives and important examples of applications compatible discretizations in computational electromagnetics, geosciences, linear elasticity, eigenvalue approximations and MHD. The contributions collected in this volume will help to elucidate relations between different methods and concepts and to generally advance our understanding of compatible spatial discretizations for PDEs. Abstracts and presentation slides from the workshop can be accessed at http://www.ima.umn.edu/talks/workshops/5-11-15.2004/.

Editors and Affiliations

  • Institute for Mathematics and its Applications, University of Minnesota, Minneapolis, USA

    Douglas N. Arnold

  • Computational Mathematics and Algorithms Department, Sandia National Laboratories, Alburquerque, USA

    Pavel B. Bochev, Richard B. Lehoucq

  • Department of Mathematical Sciences, Carnegie Mellon University, Pittsburgh, USA

    Roy A. Nicolaides

  • Theoretical Division, Los Alamos National Laboratory, Los Alamos, USA

    Mikhail Shashkov

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