Goal-oriented error estimates including algebraic errors in discontinuous Galerkin discretizations of linear boundary value problems

Vít Dolejší; Filip Roskovec

Applications of Mathematics (2017)

  • Volume: 62, Issue: 6, page 579-605
  • ISSN: 0862-7940

Abstract

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We deal with a posteriori error control of discontinuous Galerkin approximations for linear boundary value problems. The computational error is estimated in the framework of the Dual Weighted Residual method (DWR) for goal-oriented error estimation which requires to solve an additional (adjoint) problem. We focus on the control of the algebraic errors arising from iterative solutions of algebraic systems corresponding to both the primal and adjoint problems. Moreover, we present two different reconstruction techniques allowing an efficient evaluation of the error estimators. Finally, we propose a complex algorithm which controls discretization and algebraic errors and drives the adaptation of the mesh in the close to optimal manner with respect to the given quantity of interest.

How to cite

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Dolejší, Vít, and Roskovec, Filip. "Goal-oriented error estimates including algebraic errors in discontinuous Galerkin discretizations of linear boundary value problems." Applications of Mathematics 62.6 (2017): 579-605. <http://eudml.org/doc/294330>.

@article{Dolejší2017,
abstract = {We deal with a posteriori error control of discontinuous Galerkin approximations for linear boundary value problems. The computational error is estimated in the framework of the Dual Weighted Residual method (DWR) for goal-oriented error estimation which requires to solve an additional (adjoint) problem. We focus on the control of the algebraic errors arising from iterative solutions of algebraic systems corresponding to both the primal and adjoint problems. Moreover, we present two different reconstruction techniques allowing an efficient evaluation of the error estimators. Finally, we propose a complex algorithm which controls discretization and algebraic errors and drives the adaptation of the mesh in the close to optimal manner with respect to the given quantity of interest.},
author = {Dolejší, Vít, Roskovec, Filip},
journal = {Applications of Mathematics},
keywords = {quantity of interest; discontinuous Galerkin; a posteriori error estimate; algebraic error},
language = {eng},
number = {6},
pages = {579-605},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {Goal-oriented error estimates including algebraic errors in discontinuous Galerkin discretizations of linear boundary value problems},
url = {http://eudml.org/doc/294330},
volume = {62},
year = {2017},
}

TY - JOUR
AU - Dolejší, Vít
AU - Roskovec, Filip
TI - Goal-oriented error estimates including algebraic errors in discontinuous Galerkin discretizations of linear boundary value problems
JO - Applications of Mathematics
PY - 2017
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 62
IS - 6
SP - 579
EP - 605
AB - We deal with a posteriori error control of discontinuous Galerkin approximations for linear boundary value problems. The computational error is estimated in the framework of the Dual Weighted Residual method (DWR) for goal-oriented error estimation which requires to solve an additional (adjoint) problem. We focus on the control of the algebraic errors arising from iterative solutions of algebraic systems corresponding to both the primal and adjoint problems. Moreover, we present two different reconstruction techniques allowing an efficient evaluation of the error estimators. Finally, we propose a complex algorithm which controls discretization and algebraic errors and drives the adaptation of the mesh in the close to optimal manner with respect to the given quantity of interest.
LA - eng
KW - quantity of interest; discontinuous Galerkin; a posteriori error estimate; algebraic error
UR - http://eudml.org/doc/294330
ER -

References

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