Explicit estimation of error constants appearing in non-conforming linear triangular finite element method

Xuefeng Liu; Fumio Kikuchi

Applications of Mathematics (2018)

  • Volume: 63, Issue: 4, page 381-397
  • ISSN: 0862-7940

Abstract

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The non-conforming linear ( P 1 ) triangular FEM can be viewed as a kind of the discontinuous Galerkin method, and is attractive in both the theoretical and practical purposes. Since various error constants must be quantitatively evaluated for its accurate a priori and a posteriori error estimates, we derive their theoretical upper bounds and some computational results. In particular, the Babuška-Aziz maximum angle condition is required just as in the case of the conforming P 1 triangle. Some applications and numerical results are also included to see the validity and effectiveness of our analysis.

How to cite

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Liu, Xuefeng, and Kikuchi, Fumio. "Explicit estimation of error constants appearing in non-conforming linear triangular finite element method." Applications of Mathematics 63.4 (2018): 381-397. <http://eudml.org/doc/294695>.

@article{Liu2018,
abstract = {The non-conforming linear ($P_1$) triangular FEM can be viewed as a kind of the discontinuous Galerkin method, and is attractive in both the theoretical and practical purposes. Since various error constants must be quantitatively evaluated for its accurate a priori and a posteriori error estimates, we derive their theoretical upper bounds and some computational results. In particular, the Babuška-Aziz maximum angle condition is required just as in the case of the conforming $P_1$ triangle. Some applications and numerical results are also included to see the validity and effectiveness of our analysis.},
author = {Liu, Xuefeng, Kikuchi, Fumio},
journal = {Applications of Mathematics},
keywords = {FEM; non-conforming linear triangle; a priori error estimate; a posteriori error estimate; error constant; Raviart-Thomas element},
language = {eng},
number = {4},
pages = {381-397},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {Explicit estimation of error constants appearing in non-conforming linear triangular finite element method},
url = {http://eudml.org/doc/294695},
volume = {63},
year = {2018},
}

TY - JOUR
AU - Liu, Xuefeng
AU - Kikuchi, Fumio
TI - Explicit estimation of error constants appearing in non-conforming linear triangular finite element method
JO - Applications of Mathematics
PY - 2018
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 63
IS - 4
SP - 381
EP - 397
AB - The non-conforming linear ($P_1$) triangular FEM can be viewed as a kind of the discontinuous Galerkin method, and is attractive in both the theoretical and practical purposes. Since various error constants must be quantitatively evaluated for its accurate a priori and a posteriori error estimates, we derive their theoretical upper bounds and some computational results. In particular, the Babuška-Aziz maximum angle condition is required just as in the case of the conforming $P_1$ triangle. Some applications and numerical results are also included to see the validity and effectiveness of our analysis.
LA - eng
KW - FEM; non-conforming linear triangle; a priori error estimate; a posteriori error estimate; error constant; Raviart-Thomas element
UR - http://eudml.org/doc/294695
ER -

References

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