Mimetic Finite Difference Method for Elliptic Problems

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.

• 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.

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 Munch, 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)