We analyze a Discontinuous Galerkin method for a problem with linear advection-reaction and p-type diffusion, with Sobolev indices p (1,∞). The discretization of the diffusion term is based on the full gradient including jump liftings and interior-penalty stabilization while, for the advective contribution, we consider a strengthened version of the classical upwind scheme. The developed error estimates track the dependence of the local contributions to the error on the local Péclet numbers. A set of numerical tests support the theoretical derivations.
Beirao Da Veiga, L., Di Pietro, D., Haile, K. (2024). A Péclet-robust Discontinuous Galerkin method for nonlinear diffusion with advection. MATHEMATICAL MODELS AND METHODS IN APPLIED SCIENCES, 34(9 (August 2024)), 1781-1807 [10.1142/S0218202524500350].
A Péclet-robust Discontinuous Galerkin method for nonlinear diffusion with advection
Beirao Da Veiga L.;
2024
Abstract
We analyze a Discontinuous Galerkin method for a problem with linear advection-reaction and p-type diffusion, with Sobolev indices p (1,∞). The discretization of the diffusion term is based on the full gradient including jump liftings and interior-penalty stabilization while, for the advective contribution, we consider a strengthened version of the classical upwind scheme. The developed error estimates track the dependence of the local contributions to the error on the local Péclet numbers. A set of numerical tests support the theoretical derivations.
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