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

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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.

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Authors and Affiliations

  1. Department of Numerical Mathematics, Faculty of Mathematics and Physics, Charles University in Prague, Sokolovská 83, 186 75, Praha 8, Czech Republic

    Vít Dolejší & Filip Roskovec

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  1. Vít Dolejší
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  2. Filip Roskovec
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Correspondence to Vít Dolejší.

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Dedicated to Professor Miloslav Feistauer on the occasion of his 75th birthday

The research of V.Dolejší was supported by Grant No. 17-01747S of the Czech Science Foundation. The research of F.Roskovec was supported by the Charles University, project GA UK No. 92315.

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Dolejší, V., Roskovec, F. Goal-oriented error estimates including algebraic errors in discontinuous Galerkin discretizations of linear boundary value problems. Appl Math 62, 579–605 (2017). https://doi.org/10.21136/AM.2017.0173-17

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