On interpolation error on degenerating prismatic elements

Ali Khademi; Sergey Korotov; Jon Eivind Vatne

Applications of Mathematics (2018)

  • Volume: 63, Issue: 3, page 237-257
  • ISSN: 0862-7940

Abstract

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We propose an analogue of the maximum angle condition (commonly used in finite element analysis for triangular and tetrahedral meshes) for the case of prismatic elements. Under this condition, prisms in the meshes may degenerate in certain ways, violating the so-called inscribed ball condition presented by P. G. Ciarlet (1978), but the interpolation error remains of the order O ( h ) in the H 1 -norm for sufficiently smooth functions.

How to cite

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Khademi, Ali, Korotov, Sergey, and Vatne, Jon Eivind. "On interpolation error on degenerating prismatic elements." Applications of Mathematics 63.3 (2018): 237-257. <http://eudml.org/doc/294507>.

@article{Khademi2018,
abstract = {We propose an analogue of the maximum angle condition (commonly used in finite element analysis for triangular and tetrahedral meshes) for the case of prismatic elements. Under this condition, prisms in the meshes may degenerate in certain ways, violating the so-called inscribed ball condition presented by P. G. Ciarlet (1978), but the interpolation error remains of the order $O(h)$ in the $H^\{1\}$-norm for sufficiently smooth functions.},
author = {Khademi, Ali, Korotov, Sergey, Vatne, Jon Eivind},
journal = {Applications of Mathematics},
keywords = {prismatic finite element; interpolation error; semiregular family of prismatic partitions},
language = {eng},
number = {3},
pages = {237-257},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {On interpolation error on degenerating prismatic elements},
url = {http://eudml.org/doc/294507},
volume = {63},
year = {2018},
}

TY - JOUR
AU - Khademi, Ali
AU - Korotov, Sergey
AU - Vatne, Jon Eivind
TI - On interpolation error on degenerating prismatic elements
JO - Applications of Mathematics
PY - 2018
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 63
IS - 3
SP - 237
EP - 257
AB - We propose an analogue of the maximum angle condition (commonly used in finite element analysis for triangular and tetrahedral meshes) for the case of prismatic elements. Under this condition, prisms in the meshes may degenerate in certain ways, violating the so-called inscribed ball condition presented by P. G. Ciarlet (1978), but the interpolation error remains of the order $O(h)$ in the $H^{1}$-norm for sufficiently smooth functions.
LA - eng
KW - prismatic finite element; interpolation error; semiregular family of prismatic partitions
UR - http://eudml.org/doc/294507
ER -

References

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