A posteriori upper and lower error bound of the high-order discontinuous Galerkin method for the heat conduction equation

Ivana Šebestová

Applications of Mathematics (2014)

  • Volume: 59, Issue: 2, page 121-144
  • ISSN: 0862-7940

Abstract

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We deal with the numerical solution of the nonstationary heat conduction equation with mixed Dirichlet/Neumann boundary conditions. The backward Euler method is employed for the time discretization and the interior penalty discontinuous Galerkin method for the space discretization. Assuming shape regularity, local quasi-uniformity, and transition conditions, we derive both a posteriori upper and lower error bounds. The analysis is based on the Helmholtz decomposition, the averaging interpolation operator, and on the use of cut-off functions. Numerical experiments are presented.

How to cite

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Šebestová, Ivana. "A posteriori upper and lower error bound of the high-order discontinuous Galerkin method for the heat conduction equation." Applications of Mathematics 59.2 (2014): 121-144. <http://eudml.org/doc/261064>.

@article{Šebestová2014,
abstract = {We deal with the numerical solution of the nonstationary heat conduction equation with mixed Dirichlet/Neumann boundary conditions. The backward Euler method is employed for the time discretization and the interior penalty discontinuous Galerkin method for the space discretization. Assuming shape regularity, local quasi-uniformity, and transition conditions, we derive both a posteriori upper and lower error bounds. The analysis is based on the Helmholtz decomposition, the averaging interpolation operator, and on the use of cut-off functions. Numerical experiments are presented.},
author = {Šebestová, Ivana},
journal = {Applications of Mathematics},
keywords = {discontinuous Galerkin method; Helmholtz decomposition; averaging interpolation operator; Euler backward scheme; residual-based a posteriori error estimate; local cut-off function; discontinuous Galerkin method; Helmholtz decomposition; averaging interpolation operator; Euler backward scheme; residual-based a posteriori error estimate; local cut-off function; nonstationary heat conduction equation; numerical experiments},
language = {eng},
number = {2},
pages = {121-144},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {A posteriori upper and lower error bound of the high-order discontinuous Galerkin method for the heat conduction equation},
url = {http://eudml.org/doc/261064},
volume = {59},
year = {2014},
}

TY - JOUR
AU - Šebestová, Ivana
TI - A posteriori upper and lower error bound of the high-order discontinuous Galerkin method for the heat conduction equation
JO - Applications of Mathematics
PY - 2014
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 59
IS - 2
SP - 121
EP - 144
AB - We deal with the numerical solution of the nonstationary heat conduction equation with mixed Dirichlet/Neumann boundary conditions. The backward Euler method is employed for the time discretization and the interior penalty discontinuous Galerkin method for the space discretization. Assuming shape regularity, local quasi-uniformity, and transition conditions, we derive both a posteriori upper and lower error bounds. The analysis is based on the Helmholtz decomposition, the averaging interpolation operator, and on the use of cut-off functions. Numerical experiments are presented.
LA - eng
KW - discontinuous Galerkin method; Helmholtz decomposition; averaging interpolation operator; Euler backward scheme; residual-based a posteriori error estimate; local cut-off function; discontinuous Galerkin method; Helmholtz decomposition; averaging interpolation operator; Euler backward scheme; residual-based a posteriori error estimate; local cut-off function; nonstationary heat conduction equation; numerical experiments
UR - http://eudml.org/doc/261064
ER -

References

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