Lourenco Beirao da Veiga, Konstantin Lipnikov, Gianmarco's The Mimetic Finite Difference Method for Elliptic Problems PDF

By Lourenco Beirao da Veiga, Konstantin Lipnikov, Gianmarco Manzini

ISBN-10: 3319026623

ISBN-13: 9783319026626

This publication describes the theoretical and computational points of the mimetic finite distinction approach for a large classification of multidimensional elliptic difficulties, including diffusion, advection-diffusion, Stokes, elasticity, magnetostatics and plate bending difficulties. the fashionable mimetic discretization know-how constructed partly via the Authors permits one to unravel those equations on unstructured polygonal, polyhedral and generalized polyhedral meshes. The booklet offers a realistic advisor for these scientists and engineers which are drawn to the computational houses of the mimetic finite distinction strategy reminiscent of the accuracy, balance, robustness, and potency. Many examples are supplied to assist the reader to appreciate and enforce this system. This monograph additionally offers the fundamental historical past fabric and describes simple mathematical instruments required to enhance extra the mimetic discretization expertise and to increase it to numerous purposes.

Show description

Read Online or Download The Mimetic Finite Difference Method for Elliptic Problems PDF

Best counting & numeration books

Download PDF by Jiu Ding: Statistical Properties of Deterministic Systems (Tsinghua

A part of Tsinghua college Texts, "Statistical homes of Deterministic platforms" discusses the elemental thought and computational tools of the statistical houses of deterministic discrete dynamical platforms. After introducing a few easy effects from ergodic thought, difficulties relating to the dynamical process are studied: first the lifestyles of absolute non-stop invariant measures, after which their computation.

New PDF release: Earth System Modelling - Volume 2: Algorithms, Code

Accumulated articles during this sequence are devoted to the improvement and use of software program for earth procedure modelling and goals at bridging the space among IT recommendations and weather technology. the actual subject lined during this quantity addresses the old improvement, state-of-the-art and destiny views of the mathematical suggestions hired for numerical approximation of the equations describing atmospheric and oceanic movement.

Get Clifford Algebras: Geometric Modelling and Chain Geometries PDF

After revising recognized representations of the gang of Euclidean displacements Daniel Klawitter provides a finished creation into Clifford algebras. The Clifford algebra calculus is used to build new versions that let descriptions of the gang of projective modifications and inversions with admire to hyperquadrics.

Extra info for The Mimetic Finite Difference Method for Elliptic Problems

Example text

This assumption is quite natural when we deal with partial differential equations with (essential) homogeneous boundary conditions. 7) r u. Jor V' u . 8) r u. Jor (curl u) . v dV. 1. Inhomogeneous boundary conditions can be treated by extending the first-order operators to the boundary, see, for instance, [206]. The DVTC that results from this approach is different. In the mimetic approach, a problem coefficient is combined with a differential operator and the two are discretized simultaneously.

We consider again assumption (HI) from the previous section and modify assumption (H2) as follows. (H2a) The boundary data functions~, gV belong to HI/2(rD) and the dual of H~62(rN), respectively. The load function b belongs to L2(Q). Moreover, we assume that r D has positive measure. 17) is well-posed [190]. 1 holds agam. 3 Advection-diffusion equation in mixed form Many biological and geophysical problems involve transport of the scalar field c (species concentration for mass transfer in porous media or temperature for heat transfer) with the vector field f3.

We denote the sets of mesh nodes v, edges e, faces f, and polyhedra P by Y, 6', ยง, and 9, respectively. Let 2 be one of these sets. We define the subsets 2(P), 2(f), and 2( e), which are formed by the mesh objects of 2 that are related, respectively, to polyhedron P, face f, and edge e. When the argument has a higher topological dimension, the resulting set 2(P), 2(f), or 2(e) is the collection of mesh objects that belong to the boundary of P, f, and e, respectively. For example, 6'(P) denotes all the edges fonning the boundary of polyhedron P.

Download PDF sample

The Mimetic Finite Difference Method for Elliptic Problems by Lourenco Beirao da Veiga, Konstantin Lipnikov, Gianmarco Manzini


by Ronald
4.2

Rated 4.86 of 5 – based on 41 votes