Local analysis of HDG methods for convection-dominated diffusion problems

In this paper, we establish local error analysis of hybridizable discontinuous Galerkin (HDG) methods for convection-dominated diffusion equation in two types of subdomains away from the layers. The first subdomain is of O(log(1/h)h1/2)O(log(1/h)h1/2) away from the interior layers and of O(log(1/h)h)O(log(1/h)h) away from the boundary layers and the second one is of O(ϵ)O(ϵ) away from the outflow of the boundary. Our local error bound for the first subdomain can be improved by a factor of log(1/h)log(1/h). We use weighted estimates to prove the first result by constructing new weight functions and the inf–sup condition of the bilinear form to prove the second one.