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

BUSTINZA, ROMMEL; LOMBARDI, ARIEL L.; SOLANO, MANUEL

COMPUTER METHODS IN APPLIED MECHANICS AND ENGINEERING

ELSEVIER SCIENCE SA

Año: 2019 vol. 345 p. 382 - 401

0045-7825

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. In this context, when the discrete local spaces are polynomials of degree k≥0, this approach is able to recover an order of convergence [Formula presented] in L2 for all the variables, under certain assumptions on the stabilization parameter and family of triangulations. Numerical examples confirm our theoretical results.