Displaying similar documents to “About Delaunay triangulations and discrete maximum principles for the linear conforming FEM applied to the Poisson equation”

Weak discrete maximum principles

Mohammad Mujalli Al-Mahameed (2005)

Archivum Mathematicum

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We introduce weak discrete maximum principles for matrix equations associated with some elliptic problems. We also give an example on discrete maximum principles.

Inner products in covolume and mimetic methods

Kathryn A. Trapp (2008)

ESAIM: Mathematical Modelling and Numerical Analysis

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A class of compatible spatial discretizations for solving partial differential equations is presented. A discrete exact sequence framework is developed to classify these methods which include the mimetic and the covolume methods as well as certain low-order finite element methods. This construction ensures discrete analogs of the differential operators that satisfy the identities and theorems of vector calculus, in particular a Helmholtz decomposition theorem for the discrete function...

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...

Distinct equilateral triangle dissections of convex regions

Diane M. Donovan, James G. Lefevre, Thomas A. McCourt, Nicholas J. Cavenagh (2012)

Commentationes Mathematicae Universitatis Carolinae

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We define a proper triangulation to be a dissection of an integer sided equilateral triangle into smaller, integer sided equilateral triangles such that no point is the vertex of more than three of the smaller triangles. In this paper we establish necessary and sufficient conditions for a proper triangulation of a convex region to exist. Moreover we establish precisely when at least two such equilateral triangle dissections exist. We also provide necessary and sufficient conditions for...

A finite element convergence analysis for 3D Stokes equations in case of variational crimes

Petr Knobloch (2000)

Applications of Mathematics

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We investigate a finite element discretization of the Stokes equations with nonstandard boundary conditions, defined in a bounded three-dimensional domain with a curved, piecewise smooth boundary. For tetrahedral triangulations of this domain we prove, under general assumptions on the discrete problem and without any additional regularity assumptions on the weak solution, that the discrete solutions converge to the weak solution. Examples of appropriate finite element spaces are given. ...