Geodesic
Goal-oriented error estimates including algebraic errors in discontinuous Galerkin discretizations of linear boundary value problems
Applications of Mathematics, Tome 62 (2017) no. 6, pp. 579-605.

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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.
DOI : 10.21136/AM.2017.0173-17
Classification : 65N15, 65N30, 65N50
Keywords: quantity of interest; discontinuous Galerkin; a posteriori error estimate; algebraic error 
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     title = {Goal-oriented error estimates including algebraic errors in discontinuous {Galerkin} discretizations of linear boundary value problems},
     journal = {Applications of Mathematics},
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Dolejší, Vít; Roskovec, Filip. Goal-oriented error estimates including algebraic errors in discontinuous Galerkin discretizations of linear boundary value problems. Applications of Mathematics, Tome 62 (2017) no. 6, pp. 579-605. doi : 10.21136/AM.2017.0173-17. http://geodesic.mathdoc.fr/articles/10.21136/AM.2017.0173-17/

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