A posteriori error estimator for exponentially fitted Discontinuous Galerkin approximation of advection dominated problems

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The paper deals with the weakly penalized exponentially fitted incomplete interior penalty (EF-IIPG0) scheme for advection-diffusion problems. In the first part of the paper, the (Formula presented.) -matrix property on conforming weakly-acute meshes is discussed. In the second part, an a posteriori...

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Autores principales: Lombardi, A.L., Pietra, P., Prieto, M.I.
Formato: JOUR
Materias:
A posteriori estimator
Advection-diffusion equations
Discontinuous Galerkin methods
Exponentially fitted schemes
M -matrix property
Acceso en línea:http://hdl.handle.net/20.500.12110/paper_00080624_v53_n1_p83_Lombardi
Aporte de:
Biblioteca Digital - Facultad de Ciencias Exactas y Naturales (UBA) de Universidad de Buenos Aires
id todo:paper_00080624_v53_n1_p83_Lombardi
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spelling todo:paper_00080624_v53_n1_p83_Lombardi2023-10-03T14:05:51Z A posteriori error estimator for exponentially fitted Discontinuous Galerkin approximation of advection dominated problems Lombardi, A.L. Pietra, P. Prieto, M.I. A posteriori estimator Advection-diffusion equations Discontinuous Galerkin methods Exponentially fitted schemes M -matrix property The paper deals with the weakly penalized exponentially fitted incomplete interior penalty (EF-IIPG0) scheme for advection-diffusion problems. In the first part of the paper, the (Formula presented.) -matrix property on conforming weakly-acute meshes is discussed. In the second part, an a posteriori error estimate is derived. The estimator, especially designed for the advection dominated case, controls the energy norm as well as a semi-norm associated with the advective derivative, taking full advantage of the formulation on non-matching grids. The paper is supplemented by numerical experiments, where the estimator is used as local error indicator for marking the triangles to be refined in an adaptive strategy. © 2015, Springer-Verlag Italia. JOUR info:eu-repo/semantics/openAccess http://creativecommons.org/licenses/by/2.5/ar http://hdl.handle.net/20.500.12110/paper_00080624_v53_n1_p83_Lombardi
institution Universidad de Buenos Aires
institution_str I-28
repository_str R-134
collection Biblioteca Digital - Facultad de Ciencias Exactas y Naturales (UBA)
topic A posteriori estimator
Advection-diffusion equations
Discontinuous Galerkin methods
Exponentially fitted schemes
M -matrix property
spellingShingle A posteriori estimator
Advection-diffusion equations
Discontinuous Galerkin methods
Exponentially fitted schemes
M -matrix property
Lombardi, A.L.
Pietra, P.
Prieto, M.I.
A posteriori error estimator for exponentially fitted Discontinuous Galerkin approximation of advection dominated problems
topic_facet A posteriori estimator
Advection-diffusion equations
Discontinuous Galerkin methods
Exponentially fitted schemes
M -matrix property
description The paper deals with the weakly penalized exponentially fitted incomplete interior penalty (EF-IIPG0) scheme for advection-diffusion problems. In the first part of the paper, the (Formula presented.) -matrix property on conforming weakly-acute meshes is discussed. In the second part, an a posteriori error estimate is derived. The estimator, especially designed for the advection dominated case, controls the energy norm as well as a semi-norm associated with the advective derivative, taking full advantage of the formulation on non-matching grids. The paper is supplemented by numerical experiments, where the estimator is used as local error indicator for marking the triangles to be refined in an adaptive strategy. © 2015, Springer-Verlag Italia.
format JOUR
author Lombardi, A.L.
Pietra, P.
Prieto, M.I.
author_facet Lombardi, A.L.
Pietra, P.
Prieto, M.I.
author_sort Lombardi, A.L.
title A posteriori error estimator for exponentially fitted Discontinuous Galerkin approximation of advection dominated problems
title_short A posteriori error estimator for exponentially fitted Discontinuous Galerkin approximation of advection dominated problems
title_full A posteriori error estimator for exponentially fitted Discontinuous Galerkin approximation of advection dominated problems
title_fullStr A posteriori error estimator for exponentially fitted Discontinuous Galerkin approximation of advection dominated problems
title_full_unstemmed A posteriori error estimator for exponentially fitted Discontinuous Galerkin approximation of advection dominated problems
title_sort posteriori error estimator for exponentially fitted discontinuous galerkin approximation of advection dominated problems
url http://hdl.handle.net/20.500.12110/paper_00080624_v53_n1_p83_Lombardi
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AT lombardial posteriorierrorestimatorforexponentiallyfitteddiscontinuousgalerkinapproximationofadvectiondominatedproblems
AT pietrap posteriorierrorestimatorforexponentiallyfitteddiscontinuousgalerkinapproximationofadvectiondominatedproblems
AT prietomi posteriorierrorestimatorforexponentiallyfitteddiscontinuousgalerkinapproximationofadvectiondominatedproblems
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