A posteriori error estimator for exponentially fitted Discontinuous Galerkin approximation of advection dominated problems
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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Springer-Verlag Italia s.r.l.
2016
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| Acceso en línea: | Registro en Scopus DOI Handle Registro en la Biblioteca Digital |
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| LEADER | 06624caa a22005897a 4500 | ||
|---|---|---|---|
| 001 | PAPER-24510 | ||
| 003 | AR-BaUEN | ||
| 005 | 20230518205623.0 | ||
| 008 | 190411s2016 xx ||||fo|||| 00| 0 eng|d | ||
| 024 | 7 | |2 scopus |a 2-s2.0-84959116985 | |
| 040 | |a Scopus |b spa |c AR-BaUEN |d AR-BaUEN | ||
| 100 | 1 | |a Lombardi, A.L. | |
| 245 | 1 | 2 | |a A posteriori error estimator for exponentially fitted Discontinuous Galerkin approximation of advection dominated problems |
| 260 | |b Springer-Verlag Italia s.r.l. |c 2016 | ||
| 270 | 1 | 0 | |m Pietra, P.; Istituto di Matematica Applicata e Tecnologie Informatiche “Enrico Magenes”-CNR, Via Ferrata 1, Italy; email: pietra@imati.cnr.it |
| 506 | |2 openaire |e Política editorial | ||
| 504 | |a 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 | ||
| 504 | |a 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 | ||
| 504 | |a Ayuso de Dios, B., Brezzi, F., Havle, O., Marini (2012) L.D.: L2 -estimates for the DG IIPG-0 scheme. Numer. Methods Partial Differ. Equ, 28 (5), pp. 1440-1465 | ||
| 504 | |a 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 | ||
| 504 | |a 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) | ||
| 504 | |a Karakashian, O.A., Pascal, F., Convergence of adaptive discontinuous Galerkin approximations of second-order elliptic problems (2007) SIAM J. Numer. Anal., 45 (2), pp. 641-665. , (electronic) | ||
| 504 | |a Lombardi, A.L., Pietra, P., Exponentially fitted discontinuous Galerkin schemes for singularly perturbed problems (2012) Numer. Methods Partial Differ. Equ., 28 (6), pp. 1747-1777 | ||
| 504 | |a Lovadina, C., Marini, L.D., A-posteriori error estimates for discontinuous Galerkin approximations of second order elliptic problems (2009) J. Sci. Comput., 40 (1-3), pp. 340-359 | ||
| 504 | |a Roos, H.G., Stynes, M., Tobiska, L., (2008) Robust Numerical Methods for Singularly Perturbed Differential Equations: Convection-Diffusion-Reaction and Flow Problems, , Springer Series in Computational Mathematics, vol. 24, Springer, Berlin | ||
| 504 | |a Sangalli, G., Robust a-posteriori estimator for advection-diffusion-reaction problems (2008) Math. Comput., 77 (261), pp. 41-70. , (electronic) | ||
| 504 | |a Schötzau, D., Zhu, L., A robust a-posteriori error estimator for discontinuous Galerkin methods for convection-diffusion equations (2009) Appl. Numer. Math., 59 (9), pp. 2236-2255 | ||
| 504 | |a Scott, L.R., Zhang, S., Finite element interpolation of nonsmooth functions satisfying boundary conditions (1990) Math. Comput., 54 (190), pp. 483-493 | ||
| 504 | |a Verfürth, R., Robust a posteriori error estimates for stationary convection-diffusion equations (2005) SIAM J. Numer. Anal., 43 (4), pp. 1766-1782. , (electronic) | ||
| 504 | |a Zhu, L., Schötzau, D., A robust a posteriori error estimate for hp-adaptive DG methods for convection-diffusion equations (2011) IMA J. Numer. Anal., 31 (3), pp. 971-1005 | ||
| 520 | 3 | |a 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. |l eng | |
| 536 | |a Detalles de la financiación: 2011-2013, 2011-2012, IT/10/05 AR11M06 | ||
| 536 | |a Detalles de la financiación: Consejo Nacional de Investigaciones Científicas y Técnicas | ||
| 536 | |a Detalles de la financiación: The authors acknowledge partial support by the Argentine-Italy bilateral projects Innovative numerical methods for industrial problems with complex and mobile geometries funded by CNR-CONICET (2011-2012) and by MinCyT-MAE (2011-2013) IT/10/05 AR11M06. First and third authors are members of CONICET, Argentina. | ||
| 593 | |a Instituto de Ciencias, Universidad Nacional de General Sarmiento, J.M. Gutierrez 1150, Los Polvorines, Provincia de Buenos Aires B1613GSX, Argentina | ||
| 593 | |a Istituto di Matematica Applicata e Tecnologie Informatiche “Enrico Magenes”-CNR, Via Ferrata 1, Pavia, 27100, Italy | ||
| 593 | |a Departamento de Matemática, Universidad de Buenos Aires, Buenos Aires, 1428, Argentina | ||
| 690 | 1 | 0 | |a A POSTERIORI ESTIMATOR |
| 690 | 1 | 0 | |a ADVECTION-DIFFUSION EQUATIONS |
| 690 | 1 | 0 | |a DISCONTINUOUS GALERKIN METHODS |
| 690 | 1 | 0 | |a EXPONENTIALLY FITTED SCHEMES |
| 690 | 1 | 0 | |a M -MATRIX PROPERTY |
| 700 | 1 | |a Pietra, P. | |
| 700 | 1 | |a Prieto, M.I. | |
| 773 | 0 | |d Springer-Verlag Italia s.r.l., 2016 |g v. 53 |h pp. 83-103 |k n. 1 |p Calcolo |x 00080624 |t Calcolo | |
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| 856 | 4 | 0 | |u https://doi.org/10.1007/s10092-015-0138-z |y DOI |
| 856 | 4 | 0 | |u https://hdl.handle.net/20.500.12110/paper_00080624_v53_n1_p83_Lombardi |y Handle |
| 856 | 4 | 0 | |u https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_00080624_v53_n1_p83_Lombardi |y Registro en la Biblioteca Digital |
| 961 | |a paper_00080624_v53_n1_p83_Lombardi |b paper |c PE | ||
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| 999 | |c 85463 | ||