The Mimetic Finite Difference Method for Elliptic Problems

✍ Scribed by Lourenço Beirão da Veiga, Konstantin Lipnikov, Gianmarco Manzini (auth.)

• Publisher: Springer International Publishing
• Year: 2014
• Tongue: English
• Leaves: 399
• Series: MS&A - Modeling, Simulation and Applications 11
• Edition: 1
• Category: Library

✦ Synopsis

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.

✦ Table of Contents

Front Matter....Pages i-xvi
Front Matter....Pages 1-1
Model elliptic problems....Pages 3-40
Foundations of mimetic finite difference method....Pages 41-65
Mimetic inner products and reconstruction operators....Pages 67-89
Mimetic discretization of bilinear forms....Pages 91-113
Front Matter....Pages 115-115
The diffusion problem in mixed form....Pages 117-154
The diffusion problem in primal form....Pages 155-195
Maxwell’s equations....Pages 197-219
The Stokes problem....Pages 221-260
Front Matter....Pages 261-261
Elasticity and plates....Pages 263-287
Other linear and nonlinear mimetic schemes....Pages 289-310
Analysis of parameters and maximum principles....Pages 311-337
Diffusion problem on generalized polyhedral meshes....Pages 339-370
Back Matter....Pages 371-394

✦ Subjects

Computational Mathematics and Numerical Analysis; Mathematical Applications in the Physical Sciences; Partial Differential Equations; Appl.Mathematics/Computational Methods of Engineering