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Volume 2, Issue 1
Superconvergence Phenomena on Three-Dimensional Meshes

Michal Křížek

Int. J. Numer. Anal. Mod., 2 (2005), pp. 43-56.

Published online: 2005-02

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  • Abstract

We give an overview of superconvergence phenomena in the finite element method for solving three-dimensional problems, in particular, for elliptic boundary value problems of second order over uniform meshes. Some difficulties with superconvergence on tetrahedral meshes are presented as well. For a given positive integer $m$ we prove that there is no tetrahedralization of $R^3$ whose all edges are $m$-valent.

  • Keywords

linear and quadratic tetrahedral elements, acute partitions, Poisson equation, postprocessing, supercloseness, averaging and smoothing operators, regular polytopes, combinatorial topology.

  • AMS Subject Headings

65N30, 51M20

  • Copyright

COPYRIGHT: © Global Science Press

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  • TXT
@Article{IJNAM-2-43, author = {Křížek , Michal}, title = {Superconvergence Phenomena on Three-Dimensional Meshes}, journal = {International Journal of Numerical Analysis and Modeling}, year = {2005}, volume = {2}, number = {1}, pages = {43--56}, abstract = {

We give an overview of superconvergence phenomena in the finite element method for solving three-dimensional problems, in particular, for elliptic boundary value problems of second order over uniform meshes. Some difficulties with superconvergence on tetrahedral meshes are presented as well. For a given positive integer $m$ we prove that there is no tetrahedralization of $R^3$ whose all edges are $m$-valent.

}, issn = {2617-8710}, doi = {https://doi.org/}, url = {http://global-sci.org/intro/article_detail/ijnam/919.html} }
TY - JOUR T1 - Superconvergence Phenomena on Three-Dimensional Meshes AU - Křížek , Michal JO - International Journal of Numerical Analysis and Modeling VL - 1 SP - 43 EP - 56 PY - 2005 DA - 2005/02 SN - 2 DO - http://doi.org/ UR - https://global-sci.org/intro/article_detail/ijnam/919.html KW - linear and quadratic tetrahedral elements, acute partitions, Poisson equation, postprocessing, supercloseness, averaging and smoothing operators, regular polytopes, combinatorial topology. AB -

We give an overview of superconvergence phenomena in the finite element method for solving three-dimensional problems, in particular, for elliptic boundary value problems of second order over uniform meshes. Some difficulties with superconvergence on tetrahedral meshes are presented as well. For a given positive integer $m$ we prove that there is no tetrahedralization of $R^3$ whose all edges are $m$-valent.

Michal Křížek. (1970). Superconvergence Phenomena on Three-Dimensional Meshes. International Journal of Numerical Analysis and Modeling. 2 (1). 43-56. doi:
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