The Mimetic Finite Difference Method for Elliptic Problems

• Main Authors: Veiga, Lourenço Beirão da (Author), Lipnikov, Konstantin (Author), Manzini, Gianmarco (Author)
• Corporate Author: SpringerLink (Online service)
• Format: Electronic eBook
• Language: English
• Published: Cham : Springer International Publishing : Imprint: Springer, 2014.
• Series: MS&A - Modeling, Simulation and Applications, 11
• Subjects: Mathematics.; Partial differential equations.; Mathematical physics.; Computer mathematics.; Applied mathematics.; Engineering mathematics.; Computational Mathematics and Numerical Analysis.; Mathematical Applications in the Physical Sciences.; Partial Differential Equations.; Appl.Mathematics/Computational Methods of Engineering.

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 discretizatio...

Table of Contents:

• 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.