An anisotropic a priori error analysis for a convection-dominated diffusion problem using the HDG method

Abstract

This paper deals with the a priori error analysis for a convection-dominated diffusion 2D problem, when applying the HDG method on a family of anisotropic triangulations. It is known that in this case, boundary or interior layers may appear. Therefore, it is important to resolve these layers in order to recover, if possible, the expected order of approximation. In this work, we extend the use of HDG method on anisotropic meshes. To this end, some assumptions need to be asked to the stabilization parameter, as well as to the family of triangulations. In this context, when the discrete local spaces are polynomials of degree k ≥ 0, this approach is able to recover an order of convergence k + 1 2 in L 2 for all the variables. Numerical examples confirm our theoretical results.