an:05549211
Zbl 1165.65074
Ern, Alexandre; Stephansen, Annette F.; Zunino, Paolo
A discontinuous Galerkin method with weighted averages for advection-diffusion equations with locally small and anisotropic diffusivity
EN
IMA J. Numer. Anal. 29, No. 2, 235-256 (2009).
00248670
2009
j
65N30 65N12 65N15 35J25
discontinuous Galerkin method; weighted averages; locally small diffusion with advection; anisotropic diffusion; convergence; advection-diffusion equations; interior penalty scheme; high Peclet number; numerical examples
The authors consider a homogeneous Dirichlet boundary value problem for 2D and 3D advection-diffusion equations with anisotropic and discontinuous diffusivity. They introduce a symmetric weighted interior penalty scheme in the well known framework of the discontinuous Galerkin method in order to remove the difficulties induced by locally small diffusivity (high Peclet number). They prove energy convergence results which are optimal with respect to mesh size and robust with respect to diffusivity. Some numerical examples are carried out in order to underline the effectiveness of the scheme.
Calin Ioan Gheorghiu (Cluj-Napoca)