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Abstract:

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.

Registro:

Documento: Artículo
Título:A posteriori error estimator for exponentially fitted Discontinuous Galerkin approximation of advection dominated problems
Autor:Lombardi, A.L.; Pietra, P.; Prieto, M.I.
Filiación:Instituto de Ciencias, Universidad Nacional de General Sarmiento, J.M. Gutierrez 1150, Los Polvorines, Provincia de Buenos Aires B1613GSX, Argentina
Istituto di Matematica Applicata e Tecnologie Informatiche “Enrico Magenes”-CNR, Via Ferrata 1, Pavia, 27100, Italy
Departamento de Matemática, Universidad de Buenos Aires, Buenos Aires, 1428, Argentina
Palabras clave:A posteriori estimator; Advection-diffusion equations; Discontinuous Galerkin methods; Exponentially fitted schemes; M -matrix property
Año:2016
Volumen:53
Número:1
Página de inicio:83
Página de fin:103
DOI: http://dx.doi.org/10.1007/s10092-015-0138-z
Título revista:Calcolo
Título revista abreviado:Calcolo
ISSN:00080624
Registro:https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_00080624_v53_n1_p83_Lombardi

Referencias:

  • Arnold, D.N., Brezzi, F., Cockburn, B., Marini, L.D.: Unified analysis of discontinuous Galerkin methods for elliptic problems. SIAM J. Numer. Anal. 39(5), 1749–1779 (2001/02); Cangiani, A., Georgoulis, E.H., Metcalfe, S., Adaptive discontinuous Galerkin methods for nonstationary convection-diffusion problems (2014) IMA J. Numer. Anal., 34 (4), pp. 1578-1597
  • Ciarlet, P.G., (1978) Studies in Mathematics and its Applications, vol. 4, , The finite element method for elliptic problems, North-Holland Publishing Co., Amsterdam-New York-Oxford
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  • Ayuso de Dios, B., Lombardi, A.L., Pietra, P., Zikatanov, L., A block solver for the exponentially fitted IIPG-0 method (2013) Lecture Notes in Computational Science and Engineering 91, pp. 239-246
  • Houston, P., Schötzau, D., Wihler, T.P.: Energy norm a posteriori error estimation of hp -adaptive discontinuous Galerkin methods for elliptic problems. Math. Models Methods Appl. Sci. 17(1), 33–62 (2007); Karakashian, O.A., Pascal, F., A posteriori error estimates for a discontinuous Galerkin approximation of second-order elliptic problems (2003) SIAM J. Numer. Anal., 41 (6), pp. 2374-2399. , (electronic)
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Citas:

---------- APA ----------
Lombardi, A.L., Pietra, P. & Prieto, M.I. (2016) . A posteriori error estimator for exponentially fitted Discontinuous Galerkin approximation of advection dominated problems. Calcolo, 53(1), 83-103.
http://dx.doi.org/10.1007/s10092-015-0138-z
---------- CHICAGO ----------
Lombardi, A.L., Pietra, P., Prieto, M.I. "A posteriori error estimator for exponentially fitted Discontinuous Galerkin approximation of advection dominated problems" . Calcolo 53, no. 1 (2016) : 83-103.
http://dx.doi.org/10.1007/s10092-015-0138-z
---------- MLA ----------
Lombardi, A.L., Pietra, P., Prieto, M.I. "A posteriori error estimator for exponentially fitted Discontinuous Galerkin approximation of advection dominated problems" . Calcolo, vol. 53, no. 1, 2016, pp. 83-103.
http://dx.doi.org/10.1007/s10092-015-0138-z
---------- VANCOUVER ----------
Lombardi, A.L., Pietra, P., Prieto, M.I. A posteriori error estimator for exponentially fitted Discontinuous Galerkin approximation of advection dominated problems. Calcolo. 2016;53(1):83-103.
http://dx.doi.org/10.1007/s10092-015-0138-z