The Mimetic Finite Difference Method for Elliptic Problems
1st Edition
Published on 22. May 2014
XVI, 394 pages
978-3-319-02663-3 (ISBN)
Description
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.
Reviews / Votes
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)More details
Series
Language
English
Place of publication
Cham
Switzerland
Publishing group
Springer International Publishing
Target group
Professional and scholarly
Product notice
Reflowable
Illustrations
XVI, 394 p. 107 illus., 59 illus. in color.
File size
33,69 MB
ISBN-13
978-3-319-02663-3 (9783319026633)
DOI
10.1007/978-3-319-02663-3
Schweitzer Classification
Other editions
Additional editions
Lourenco Beirao Da Veiga | Konstantin Lipnikov | Gianmarco Manzini
The Mimetic Finite Difference Method for Elliptic Problems
Book
12/2013
Springer
€106.99
Shipment within 10-15 days
Persons
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.
Content
1 Model elliptic problems.- 2 Foundations of mimetic finite difference method.- 3 Mimetic inner products and reconstruction operators.- 4 Mimetic discretization of bilinear forms.- 5 The diffusion problem in mixed form.- 6 The diffusion problem in primal form.- 7 Maxwells equations. 8. The Stokes problem. 9 Elasticity and plates.- 10 Other linear and nonlinear mimetic schemes.- 11 Analysis of parameters and maximum principles.- 12 Diffusion problem on generalized polyhedral meshes.
