Abstract
In this paper, we provide a projection-based analysis of the h-version of the hybridizable discontinuous Galerkin methods for convection-diffusion equations on semimatching nonconforming meshes made of simplexes; the degrees of the piecewise polynomials are allowed to vary from element to element. We show that, for approximations of degree k on all elements, the order of convergence of the error in the diffusive flux is k + 1 and that of a projection of the error in the scalar unknown is 1 for k = 0 and k + 2 for k > 0. We also show that, for the variable-degree case, the projection of the error in the scalar variable is h times the projection of the error in the vector variable, provided a simple condition is satisfied for the choice of the degree of the approximation on the elements with hanging nodes. These results hold for any ( bounded) irregularity index of the nonconformity of the mesh. Moreover, our analysis can be extended to hypercubes.