A posteriori error estimator for exponentially fitted Discontinuous Galerkin approximation of advection dominated problems

作者：Lombardi Ariel L; Pietra Paola^*; Prieto Mariana I

来源：Calcolo, 2016, 53(1): 83-103.

DOI：10.1007/s10092-015-0138-z

• Discontinuous Galerkin methods
• Exponentially fitted schemes
• Advection-diffusion equations
• A posteriori estimator
• M-matrix property

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 seminorm 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.

• 出版日期2016-3