An adaptive enrichment algorithm for advection-dominated problems.
ABGRALL, Remi
Parallel tools for Numerical Algorithms and Resolution of essentially Hyperbolic problems [BACCHUS]
Institut de Mathématiques de Bordeaux [IMB]
Parallel tools for Numerical Algorithms and Resolution of essentially Hyperbolic problems [BACCHUS]
Institut de Mathématiques de Bordeaux [IMB]
KRUST, Arnaud
Institut de Mathématiques de Bordeaux [IMB]
Parallel tools for Numerical Algorithms and Resolution of essentially Hyperbolic problems [BACCHUS]
Institut de Mathématiques de Bordeaux [IMB]
Parallel tools for Numerical Algorithms and Resolution of essentially Hyperbolic problems [BACCHUS]
ABGRALL, Remi
Parallel tools for Numerical Algorithms and Resolution of essentially Hyperbolic problems [BACCHUS]
Institut de Mathématiques de Bordeaux [IMB]
Parallel tools for Numerical Algorithms and Resolution of essentially Hyperbolic problems [BACCHUS]
Institut de Mathématiques de Bordeaux [IMB]
KRUST, Arnaud
Institut de Mathématiques de Bordeaux [IMB]
Parallel tools for Numerical Algorithms and Resolution of essentially Hyperbolic problems [BACCHUS]
< Reduce
Institut de Mathématiques de Bordeaux [IMB]
Parallel tools for Numerical Algorithms and Resolution of essentially Hyperbolic problems [BACCHUS]
Language
en
Rapport
This item was published in
2012-01p. 24
English Abstract
We are interested in developing a numerical framework well suited for advection-diffusion problems when the advection part is dominant. In that case, given Dirichlet type boundary condition, it is well known that a boundary ...Read more >
We are interested in developing a numerical framework well suited for advection-diffusion problems when the advection part is dominant. In that case, given Dirichlet type boundary condition, it is well known that a boundary layer develops. In order to resolve correctly this layer, standard methods consist in increasing the mesh resolution and possibly increasing the formal accuracy of the numerical method. In this paper, we follow another path: we do not seek to increase the formal accuracy of the scheme but, by a careful choice of finite element, to lower the mesh resolution in the layer. Indeed the finite element representation we choose is locally the sum of a standard one plus an enrichment. This paper proposes such a method and with several numerical examples, we show the potential of this approach. In particular we show that the method is not very sensitive to the choice of the enrichment.Read less <
English Keywords
enrichment
adaptivity
stabilized finite elements
XFEM
boundary-layer
European Project
Adaptive Schemes for Deterministic and Stochastic Flow Problems
Origin
Hal imported