CONVERGENCE OF MIMETIC FINITE DIFFERENCE METHOD FOR DIFFUSION PROBLEMS ON POLYHEDRAL MESHES WITH CURVED FACES

2006 ◽  
Vol 16 (02) ◽  
pp. 275-297 ◽  
Author(s):  
FRANCO BREZZI ◽  
KONSTANTIN LIPNIKOV ◽  
MIKHAIL SHASHKOV
Keyword(s):  
Finite Difference ◽  
Material Properties ◽  
Variable Pressure ◽  
First Order ◽  
Polyhedral Meshes ◽  
Vector Variable ◽  
Scalar Variable ◽  
Mimetic Finite Difference Method ◽  
Convergence Estimates ◽  
Diffusion Problems

New mimetic finite difference discretizations of diffusion problems on unstructured polyhedral meshes with strongly curved (non-planar) faces are developed. The material properties are described by a full tensor. The optimal convergence estimates, the second order for a scalar variable (pressure) and the first order for a vector variable (velocity), are proved.

A FAMILY OF MIMETIC FINITE DIFFERENCE METHODS ON POLYGONAL AND POLYHEDRAL MESHES

2005 ◽  
Vol 15 (10) ◽  
pp. 1533-1551 ◽  
Author(s):  
FRANCO BREZZI ◽  
KONSTANTIN LIPNIKOV ◽  
VALERIA SIMONCINI
Keyword(s):  
Finite Difference ◽  
Material Properties ◽  
Numerical Experiments ◽  
Finite Difference Methods ◽  
Polyhedral Meshes ◽  
Discretization Schemes ◽  
Difference Methods ◽  
Theoretical Results ◽  
Diffusion Problems

A family of inexpensive discretization schemes for diffusion problems on unstructured polygonal and polyhedral meshes is introduced. The material properties are described by a full tensor. The theoretical results are confirmed with numerical experiments.

Analysis of a New Mixed Finite Volume Method

2003 ◽  
Vol 3 (1) ◽  
pp. 189-201 ◽  
Author(s):  
Ilya D. Mishev
Keyword(s):  
Finite Volume Method ◽  
Finite Volume ◽  
Elliptic Equations ◽  
Variable Pressure ◽  
Order Error ◽  
First Order ◽  
Scalar Variable ◽  
Volume Method ◽  
Well Posed ◽  
Theoretical Results

AbstractA new mixed finite volume method for elliptic equations with tensor coefficients on rectangular meshes (2 and 3-D) is presented. The implementation of the discretization as a finite volume method for the scalar variable (“pressure”) is derived. The scheme is well suited for heterogeneous and anisotropic media because of the generalized harmonic averaging. It is shown that the method is stable and well posed. First-order error estimates are derived. The theoretical results are confirmed by the presented numerical experiments.

Analysis and design of thermo-mechanical interfaces

2012 ◽  
Vol 60 (2) ◽  
pp. 205-213
Author(s):  
K. Dems ◽  
Z. Mróz
Keyword(s):  
Optimality Conditions ◽  
Mechanical Loading ◽  
Material Properties ◽  
Structural Response ◽  
External Boundary ◽  
Mechanical Loads ◽  
Internal Interface ◽  
Analysis And Design ◽  
First Order ◽  
Mechanical Nature

Abstract. An elastic structure subjected to thermal and mechanical loading with prescribed external boundary and varying internal interface is considered. The different thermal and mechanical nature of this interface is discussed, since the interface form and its properties affect strongly the structural response. The first-order sensitivities of an arbitrary thermal and mechanical behavioral functional with respect to shape and material properties of the interface are derived using the direct or adjoint approaches. Next the relevant optimality conditions are formulated. Some examples illustrate the applicability of proposed approach to control the structural response due to applied thermal and mechanical loads.

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