MS&A

The Mimetic Finite Difference Method for Elliptic Problems

Authors: Beirao da Veiga, Lourenco, Lipnikov, Konstantin, Manzini, Gianmarco

  • This is the first book on modern mimetic technology
  • The theoretical analysis is complemented by simple examples
  • The book covers a broad range of applications
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eBook $99.00
price for USA (gross)
  • ISBN 978-3-319-02663-3
  • Digitally watermarked, DRM-free
  • Included format: PDF, EPUB
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
Hardcover $129.00
price for USA
  • ISBN 978-3-319-02662-6
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
Softcover $129.00
price for USA
  • Customers within the U.S. and Canada please contact Customer Service at 1-800-777-4643, Latin America please contact us at +1-212-460-1500 (Weekdays 8:30am – 5:30pm ET) to place your order.
  • Due: October 14, 2016
  • ISBN 978-3-319-37900-5
  • Free shipping for individuals worldwide
Rent the ebook  
  • Rental duration: 1 or 6 month
  • low-cost access
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About this book

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.

About the authors

The Authors are active researchers in the field of numerical discretizations of partial differential equations. Together and in collaboration with other researchers, they published more than one-hundred papers on ISI ranked journals. Therefore, their expertise spans the formal mathematical analysis of the mimetic discretization methods, the application of this theoretical framework to real scientific and engineering models formulated in the setting of elliptic problems, and the computational properties of the numerical schemes discussed in the book.

Reviews

From the book reviews:

“This book of about 400 pages is clear and relatively easy to read. It shows the capabilities and the efficiency of the mimetic finite difference method in the resolution of the usual partial differential equations, from their strong formulation. Many theoretical and practical aspects are addressed in detail. It is therefore highly recommended for anyone who wants to learn and use this method.” (Arnaud Münch, Mathematical Reviews, October, 2014)

“The research monograph is a useful source for scientists and engineers interested in computational treatment for various mathematical models arising in real life. It also proves to be a valuable research monograph for graduate students in Applied Mathematics or Computational Physics.” (Marius Ghergu, zbMATH, Vol. 1286, 2014)

Table of contents (12 chapters)

  • Model elliptic problems

    Veiga, Lourenço Beirão (et al.)

    Pages 3-40

  • Foundations of mimetic finite difference method

    Veiga, Lourenço Beirão (et al.)

    Pages 41-65

  • Mimetic inner products and reconstruction operators

    Veiga, Lourenço Beirão (et al.)

    Pages 67-89

  • Mimetic discretization of bilinear forms

    Veiga, Lourenço Beirão (et al.)

    Pages 91-113

  • The diffusion problem in mixed form

    Veiga, Lourenço Beirão (et al.)

    Pages 117-154

Buy this book

eBook $99.00
price for USA (gross)
  • ISBN 978-3-319-02663-3
  • Digitally watermarked, DRM-free
  • Included format: PDF, EPUB
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
Hardcover $129.00
price for USA
  • ISBN 978-3-319-02662-6
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
Softcover $129.00
price for USA
  • Customers within the U.S. and Canada please contact Customer Service at 1-800-777-4643, Latin America please contact us at +1-212-460-1500 (Weekdays 8:30am – 5:30pm ET) to place your order.
  • Due: October 14, 2016
  • ISBN 978-3-319-37900-5
  • Free shipping for individuals worldwide
Rent the ebook  
  • Rental duration: 1 or 6 month
  • low-cost access
  • online reader with highlighting and note-making option
  • can be used across all devices
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Bibliographic Information

Bibliographic Information
Book Title
The Mimetic Finite Difference Method for Elliptic Problems
Authors
Series Title
MS&A
Series Volume
11
Copyright
2014
Publisher
Springer International Publishing
Copyright Holder
Springer International Publishing Switzerland
eBook ISBN
978-3-319-02663-3
DOI
10.1007/978-3-319-02663-3
Hardcover ISBN
978-3-319-02662-6
Softcover ISBN
978-3-319-37900-5
Series ISSN
2037-5255
Edition Number
1
Number of Pages
XVI, 394
Number of Illustrations and Tables
48 b/w illustrations, 59 illustrations in colour
Topics