Displaying similar documents to “Simplicial finite elements in higher dimensions”

What is the smallest possible constant in Céa's lemma?

Wei Chen, Michal Křížek (2006)

Applications of Mathematics

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We consider finite element approximations of a second order elliptic problem on a bounded polytopic domain in ℝ d with d ∈ { 1 , 2 , 3 , ... } . The constant C ≥ 1 appearing in Céa’s lemma and coming from its standard proof can be very large when the coefficients of an elliptic operator attain considerably different values. We restrict ourselves to regular families of uniform partitions and linear simplicial elements. Using a lower bound of the interpolation error and the supercloseness between the finite element...

Mimetic finite differences for elliptic problems

Franco Brezzi, Annalisa Buffa, Konstantin Lipnikov (2009)

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

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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.

On discontinuous Galerkin method and semiregular family of triangulations

Aleš Prachař (2006)

Applications of Mathematics

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Discretization of second order elliptic partial differential equations by discontinuous Galerkin method often results in numerical schemes with penalties. In this paper we analyze these penalized schemes in the context of quite general triangular meshes satisfying only a semiregularity assumption. A new (modified) penalty term is presented and theoretical properties are proven together with illustrative numerical results.

The discrete maximum principle for Galerkin solutions of elliptic problems

Tomáš Vejchodský (2012)

Open Mathematics

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This paper provides an equivalent characterization of the discrete maximum principle for Galerkin solutions of general linear elliptic problems. The characterization is formulated in terms of the discrete Green’s function and the elliptic projection of the boundary data. This general concept is applied to the analysis of the discrete maximum principle for the higher-order finite elements in one-dimension and to the lowest-order finite elements on simplices of arbitrary dimension. The...