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Mimetic finite differences for elliptic problems

Franco Brezzi, Annalisa Buffa, Konstantin Lipnikov (2009)

ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique

We developed a mimetic finite difference method for solving elliptic equations with tensor coefficients on polyhedral meshes. The first-order convergence estimates in a mesh-dependent H 1 norm are derived.

Mimetic finite differences for elliptic problems

Franco Brezzi, Annalisa Buffa, Konstantin Lipnikov (2008)

ESAIM: Mathematical Modelling and Numerical Analysis

We developed a mimetic finite difference method for solving elliptic equations with tensor coefficients on polyhedral meshes. The first-order convergence estimates in a mesh-dependent H1 norm are derived.

Minimal Graphs in n × and n + 1

Ricardo Sà Earp, Eric Toubiana (2010)

Annales de l’institut Fourier

We construct geometric barriers for minimal graphs in n × . We prove the existence and uniqueness of a solution of the vertical minimal equation in the interior of a convex polyhedron in n extending continuously to the interior of each face, taking infinite boundary data on one face and zero boundary value data on the other faces.In n × , we solve the Dirichlet problem for the vertical minimal equation in a C 0 convex domain Ω n taking arbitrarily continuous finite boundary and asymptotic boundary data.We prove...

Module structure in Conley theory with some applications

Zdzisław Dzedzej (2014)

Banach Center Publications

A multiplicative structure in the cohomological version of Conley index is described following a joint paper by the author with K. Gęba and W. Uss. In the case of equivariant flows we apply a normalization procedure known from equivariant degree theory and we propose a new continuation invariant. The theory is applied then to obtain a mountain pass type theorem. Another illustrative application is a result on multiple bifurcations for some elliptic PDE.

Monotone operators in divergence form with x -dependent multivalued graphs

Gilles Francfort, François Murat, Luc Tartar (2004)

Bollettino dell'Unione Matematica Italiana

We prove the existence of solutions to - div a x , grad u = f , together with appropriate boundary conditions, whenever a x , e is a maximal monotone graph in e , for every fixed x . We propose an adequate setting for this problem, in particular as far as measurability is concerned. It consists in looking at the graph after a 45 rotation, for every fixed x ; in other words, the graph d a x , e is defined through d - e = φ x , d + e , where φ is a Carathéodory contraction in R N . This definition is shown to be equivalent to the fact that a ( x , ) is pointwise monotone...

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