The paper deals with the weakly penalized exponentially fitted incomplete interior penalty (EF-IIPG0) scheme for advection-diffusion problems. In the first part of the paper, the M -matrix property on conforming weakly-acute meshes is discussed. In the second part, an a posteriori error estimate is derived. The estimator, especially designed for the advection dominated case, controls the energy norm as well as a semi-norm associated with the advective derivative, taking full advantage of the formulation on non-matching grids. The paper is supplemented by numerical experiments, where the estimator is used as local error indicator for marking the triangles to be refined in an adaptive strategy.
A-posteriori error estimator for exponentially fitted discontinuous Galerkin approximation for advection dominated problems
AL Lombardi;P Pietra;
2016
Abstract
The paper deals with the weakly penalized exponentially fitted incomplete interior penalty (EF-IIPG0) scheme for advection-diffusion problems. In the first part of the paper, the M -matrix property on conforming weakly-acute meshes is discussed. In the second part, an a posteriori error estimate is derived. The estimator, especially designed for the advection dominated case, controls the energy norm as well as a semi-norm associated with the advective derivative, taking full advantage of the formulation on non-matching grids. The paper is supplemented by numerical experiments, where the estimator is used as local error indicator for marking the triangles to be refined in an adaptive strategy.I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.
