A Projection-Based Error Analysis of HDG Methods for a Partially Coupled Elliptic Problem

Abstract

A technique for the error analysis of hibridizable discontinuous Galerkin methods (HDG) is applied to analyze a model for the semiconductor thermal device when the source is null or constant a particular model for flow in a porous medium when the general sources, more directly, we say that we are dealing here with a partially coupled problem, i.e. coupled in a single direction. The techinique relies on the use of a projection whose design is inspired the form of the numerical traces of the methods. When this technique appeared in the literature in (Cockburn, Gopalakrishnan and Sayas), the authors performed an analysis an analysis for an elliptical problem, is this work we will analyze for a problem consisting of two partially coupled elliptical problems. The differences, comparing our analysis with the previous analysis of literature, arise only in the heat equation that, is coupled to the potential, this is because the coupling is only unidirectional, that is, the system is coupled only by the heat source that depends on the square of the charge flow modulus.