On polynomial robustness of flux reconstructions

Miloslav Vlasák

Applications of Mathematics (2020)

  • Volume: 65, Issue: 2, page 153-172
  • ISSN: 0862-7940

Abstract

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We deal with the numerical solution of elliptic not necessarily self-adjoint problems. We derive a posteriori upper bound based on the flux reconstruction that can be directly and cheaply evaluated from the original fluxes and we show for one-dimensional problems that local efficiency of the resulting a posteriori error estimators depends on p 1 / 2 only, where p is the discretization polynomial degree. The theoretical results are verified by numerical experiments.

How to cite

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Vlasák, Miloslav. "On polynomial robustness of flux reconstructions." Applications of Mathematics 65.2 (2020): 153-172. <http://eudml.org/doc/297176>.

@article{Vlasák2020,
abstract = {We deal with the numerical solution of elliptic not necessarily self-adjoint problems. We derive a posteriori upper bound based on the flux reconstruction that can be directly and cheaply evaluated from the original fluxes and we show for one-dimensional problems that local efficiency of the resulting a posteriori error estimators depends on $p^\{1/2\}$ only, where $p$ is the discretization polynomial degree. The theoretical results are verified by numerical experiments.},
author = {Vlasák, Miloslav},
journal = {Applications of Mathematics},
keywords = {a posteriori error estimate; $p$-robustness; elliptic problem},
language = {eng},
number = {2},
pages = {153-172},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {On polynomial robustness of flux reconstructions},
url = {http://eudml.org/doc/297176},
volume = {65},
year = {2020},
}

TY - JOUR
AU - Vlasák, Miloslav
TI - On polynomial robustness of flux reconstructions
JO - Applications of Mathematics
PY - 2020
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 65
IS - 2
SP - 153
EP - 172
AB - We deal with the numerical solution of elliptic not necessarily self-adjoint problems. We derive a posteriori upper bound based on the flux reconstruction that can be directly and cheaply evaluated from the original fluxes and we show for one-dimensional problems that local efficiency of the resulting a posteriori error estimators depends on $p^{1/2}$ only, where $p$ is the discretization polynomial degree. The theoretical results are verified by numerical experiments.
LA - eng
KW - a posteriori error estimate; $p$-robustness; elliptic problem
UR - http://eudml.org/doc/297176
ER -

References

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