Displaying similar documents to “On the existence of strongly regular families of triangulations for domains with a piecewise smooth boundary”

How to recover the gradient of linear elements on nonuniform triangulations

Ivan Hlaváček, Michal Křížek, Vladislav Pištora (1996)

Applications of Mathematics

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We propose and examine a simple averaging formula for the gradient of linear finite elements in R d whose interpolation order in the L q -norm is 𝒪 ( h 2 ) for d < 2 q and nonuniform triangulations. For elliptic problems in R 2 we derive an interior superconvergence for the averaged gradient over quasiuniform triangulations. A numerical example is presented.

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...