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Lombardi, Ariel L.; Pietra, Paola; Prieto, Mariana I.

A posteriori error estimator for exponentially fitted discontinuous Galerkin approximation of advection dominated problems. (English) Zbl 1336.65182

Calcolo 53, No. 1, 83-103 (2016).
B. Ayuso de Dios et al. [“A block solver for the exponentially fitted IIPG-0 method”, arXiv:1107.2831] had proposed a block solver for a weakly penalized exponentially fitted incomplete-interior-penalty (EF-IIPG0) scheme on conforming meshes. The main result presented here is on the design and the analysis of an a posteriori error estimator for the EF-IIPG0 discretization scheme, allowing for non-matching grids. The estimator so obtained is used as local error indicator for marking the triangles to be refined (or derefined) in an adaptive strategy. The analysis given here follows the approach of D. Schötzau and L. Zhu [Appl. Numer. Math. 59, No. 9, 2236–2255 (2009; Zbl 1169.65108)], where the error is split into a conforming part and a (discontinuous) remainder. Some numerical experiments using the a posteriori error estimates as error indicator for an adaptive refinement strategy are also given.
Reviewer: H. P. Dikshit (Bhopal)

MSC:

65N15 Error bounds for boundary value problems involving PDEs
65N30 Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs
35J25 Boundary value problems for second-order elliptic equations
65N50 Mesh generation, refinement, and adaptive methods for boundary value problems involving PDEs

Keywords:

discontinuous Galerkin methods; exponentially fitted schemes; advection-diffusion equations; a posteriori error estimator; \(M\)-matrix property; numerical experiment; adaptive refinement

Citations:

Zbl 1169.65108
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Full Text: DOI

References:

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