AN ANISOTROPIC A PRIORI ERROR ANALYSIS FOR A CONVECTION DIFFUSION PROBLEM USING AN HDG METHOD

BUSTINZA, ROMMEL; LOMBARDI, ARIEL LUIS; SOLANO, MANUEL

Londres

Conferencia; Conference on the Mathematics of Finite Elements and Applications MAFELAP 2016; 2016

Brunel University London

(Expositor: Rommel Bustinza) In this talk we present an a priori error analysis for a convection diffusion problem, considering an HDG method and a family of anisotropic triangulation. As result, we deduce that when diffusion is dominant, the behaviour of the method (considering k as degree of approximation for every unknown) is such that the global L2−norm of the error of the scalar and vector unknowns converge with order k +1, while the unknown related to the trace of scalar unknown, on the skeleton of the mesh, does with order k + 2. For convection dominated diffusion equation, isotropic triangulations are not suitable. However, the use of anisotropic meshes let us to recover the convergence of the method, once the boundary or inner layer is solved. Numerical examples confirm these theoretical results.