http://www.cnr.it/ontology/cnr/individuo/prodotto/ID202411
A unified approach for handling convection terms in finite volumes and mimetic discretization methods for elliptic problems (Articolo in rivista)
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- A unified approach for handling convection terms in finite volumes and mimetic discretization methods for elliptic problems (Articolo in rivista) (literal)
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- 2011-01-01T00:00:00+01:00 (literal)
- Http://www.cnr.it/ontology/cnr/pubblicazioni.owl#doi
- 10.1093/imanum/drq018 (literal)
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Beirao da Veiga L., Droniou J., Manzini G. (2011)
A unified approach for handling convection terms in finite volumes and mimetic discretization methods for elliptic problems
in IMA journal of numerical analysis; Oxford University Press, Oxford (Regno Unito)
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- Beirao da Veiga L., Droniou J., Manzini G. (literal)
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- http://imajna.oxfordjournals.org/content/31/4/1357 (literal)
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- Dipartimento di Matematica F. Enriques, Università Degli Studi di Milano; Institut de Mathématiques et de Modélisation de Montpellier, Université Montpellier ; Istituto di Matematica Applicata e Tecnologie Informatiche - CNR, Pavia. (literal)
- Titolo
- A unified approach for handling convection terms in finite volumes and mimetic discretization methods for elliptic problems (literal)
- Abstract
- We study the numerical approximation to the solution of the steady convection-diffusion equation. The diffusion term is discretized by using the hybrid mimetic method (HMM), which is the unified formulation for the hybrid finite-volume (FV) method, the mixed FV method and the mimetic finite-difference method recently proposed in Droniou et al. (2010, Math. Models Methods Appl. Sci., 20, 265-295). In such a setting we discuss several techniques to discretize the convection term that are mainly adapted from the literature on FV or FV schemes. For this family of schemes we provide a full proof of convergence under very general regularity conditions of the solution field and derive an error estimate when the scalar solution is in H 2(?). Finally, we compare the performance of these schemes on a set of test cases selected from the literature in order to document the accuracy of the numerical approximation in both diffusion- and convection-dominated regimes. Moreover, we numerically investigate the behaviour of these methods in the approximation of solutions with boundary layers or internal regions with strong gradients. (literal)
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