© 2006

Compatible Spatial Discretizations

  • Douglas N. Arnold
  • Pavel B. Bochev
  • Richard B. Lehoucq
  • Roy A. Nicolaides
  • Mikhail Shashkov
  • 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

Conference proceedings

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

Table of contents

  1. Front Matter
    Pages i-xiv
  2. Ivar Aavatsmark, Geir Terje Eigestad, Runhild Aae Klausen
    Pages 1-21
  3. Douglas N. Arnold, Richard S. Falk, Ragnar Winther
    Pages 23-46
  4. Douglas N. Arnold, Richard S. Falk, Ragnar Winther
    Pages 47-67
  5. Pavel B. Bochev, James M. Hyman
    Pages 89-119
  6. R. A. Nicolaides, K. A. Trapp
    Pages 161-171
  7. J. Blair Perot, Dragan Vidovic, Pieter Wesseling
    Pages 173-188
  8. Mary F. Wheeler, Ivan Yotov
    Pages 189-207
  9. Daniel A. White, Joseph M. Koning, Robert N. Rieben
    Pages 209-234
  10. Back Matter
    Pages 235-247

About these proceedings


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


Finite Maxwell's equations Topology equation finite element method linear optimization partial differential equation

Editors and affiliations

  • Douglas N. Arnold
    • 1
  • Pavel B. Bochev
    • 2
  • Richard B. Lehoucq
    • 2
  • Roy A. Nicolaides
    • 3
  • Mikhail Shashkov
    • 4
  1. 1.Institute for Mathematics and its ApplicationsUniversity of MinnesotaMinneapolisUSA
  2. 2.Computational Mathematics and Algorithms DepartmentSandia National LaboratoriesAlburquerqueUSA
  3. 3.Department of Mathematical SciencesCarnegie Mellon UniversityPittsburghUSA
  4. 4.Theoretical DivisionLos Alamos National LaboratoryLos AlamosUSA

Bibliographic information