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The Mimetic Finite Difference Method for Elliptic Problems

  • Lourenço Beirão da Veiga
  • Konstantin Lipnikov
  • Gianmarco Manzini

Part of the MS&A - Modeling, Simulation and Applications book series (MS&A, volume 11)

Table of contents

  1. Front Matter
    Pages i-xvi
  2. Foundation

    1. Front Matter
      Pages 1-1
    2. Lourenço Beirão da Veiga, Konstantin Lipnikov, Gianmarco Manzini
      Pages 3-40
    3. Lourenço Beirão da Veiga, Konstantin Lipnikov, Gianmarco Manzini
      Pages 41-65
    4. Lourenço Beirão da Veiga, Konstantin Lipnikov, Gianmarco Manzini
      Pages 67-89
    5. Lourenço Beirão da Veiga, Konstantin Lipnikov, Gianmarco Manzini
      Pages 91-113
  3. Mimetic Discretization of Basic PDEs

    1. Front Matter
      Pages 115-115
    2. Lourenço Beirão da Veiga, Konstantin Lipnikov, Gianmarco Manzini
      Pages 117-154
    3. Lourenço Beirão da Veiga, Konstantin Lipnikov, Gianmarco Manzini
      Pages 155-195
    4. Lourenço Beirão da Veiga, Konstantin Lipnikov, Gianmarco Manzini
      Pages 197-219
    5. Lourenço Beirão da Veiga, Konstantin Lipnikov, Gianmarco Manzini
      Pages 221-260
  4. Further Developments

    1. Front Matter
      Pages 261-261
    2. Lourenço Beirão da Veiga, Konstantin Lipnikov, Gianmarco Manzini
      Pages 263-287
    3. Lourenço Beirão da Veiga, Konstantin Lipnikov, Gianmarco Manzini
      Pages 289-310
    4. Lourenço Beirão da Veiga, Konstantin Lipnikov, Gianmarco Manzini
      Pages 311-337
    5. Lourenço Beirão da Veiga, Konstantin Lipnikov, Gianmarco Manzini
      Pages 339-370
  5. Back Matter
    Pages 371-394

About this book

Introduction

This book describes the theoretical and computational aspects of the mimetic finite difference method for a wide class of multidimensional elliptic problems, which includes diffusion, advection-diffusion, Stokes, elasticity, magnetostatics and plate bending problems. The modern mimetic discretization technology developed in part by the Authors allows one to solve these equations on unstructured polygonal, polyhedral and generalized polyhedral meshes. The book provides a practical guide for those scientists and engineers that are interested in the computational properties of the mimetic finite difference method such as the accuracy, stability, robustness, and efficiency. Many examples are provided to help the reader to understand and implement this method. This monograph also provides the essential background material and describes basic mathematical tools required to develop further the mimetic discretization technology and to extend it to various applications.

Keywords

compatible discretizations convergence analysis discrete vector and tensor calculus partial differential equations polyhedral and polygonal meshes

Authors and affiliations

  • Lourenço Beirão da Veiga
    • 1
  • Konstantin Lipnikov
    • 2
  • Gianmarco Manzini
    • 2
  1. 1.Dipartimento di Matematica “Federico Enriques”Università degli Studi di MilanoItaly
  2. 2.Theoretical DivisionLos Alamos National LaboratoryUSA

Bibliographic information

  • DOI https://doi.org/10.1007/978-3-319-02663-3
  • Copyright Information Springer International Publishing Switzerland 2014
  • Publisher Name Springer, Cham
  • eBook Packages Mathematics and Statistics
  • Print ISBN 978-3-319-02662-6
  • Online ISBN 978-3-319-02663-3
  • Series Print ISSN 2037-5255
  • Series Online ISSN 2037-5263
  • Buy this book on publisher's site