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Cite Details

Markus Berndt, Konstantin Lipnikov, Pavel Vachal and Mikhail Shashkov, "A Node Reconnection Algorithm for Mimetic Finite Difference Discretizations of Elliptic Equations on Triangular Meshes ", Communications in Mathematical Sciences, vol. 3, no. 4, pp. 665-680, 2005

Abstract

Most efficient adaptive mesh methods employ only a few strategies, including local mesh refinement (h-adaptation), movement of mesh nodes (r-adaptation), and node reconnection (c-adaptation). Despite of its simplicity, node reconnection is the least popular of the three. However, using only node reconnection the discretization error can be significantly reduced. In this paper, we develop and numerically analyze a new c-adaptation algorithm for mimetic finite difference discretizations of elliptic equations on triangular meshes. Our algorithm is based on a new error indicator for such discretizations, which can also be used for unstructured general polygonal meshes. We demonstrate the efficiency of our new algorithm with numerical examples.

BibTeX Entry

@article{berndt-2004-noderecon,
author = {Markus Berndt and Konstantin Lipnikov and Pavel Vachal and Mikhail Shashkov},
title = {A Node Reconnection Algorithm for Mimetic Finite Difference Discretizations of Elliptic Equations on Triangular Meshes },
year = {2005},
urlpdf = {http://intlpress.com/CMS/issue3-4/CMS_3_665_680.pdf},
journal = {Communications in Mathematical Sciences},
volume = {3},
number = {4},
pages = {665-680}
}