Tutorial on Hybridizable Discontinuous Galerkin (HDG) for Second-Order Elliptic Problems

Author (s): Sevilla, R. and Huerta. A.
Journal: Advanced Finite Element Technologies, Springer International Publishing

Volume: 566
Pages: 105 – 129
Date: 2016

Abstract:
The HDG is a new class of discontinuous Galerkin (DG) methods that shares favorable properties with classical mixed methods such as the well known Raviart-Thomas methods. In particular, HDG provides optimal convergence of both the primal and the dual variables of the mixed formulation. This property enables the construction of superconvergent solutions, contrary to other popular DG methods. In addition, its reduced computational cost, compared to other DG methods, has made HDG an attractive alternative for solving problems governed by partial differential equations.

A tutorial on HDG for the numerical solution of second-order elliptic problems is presented. Particular emphasis is placed on providing all the necessary details for the implementation of HDG methods.

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Bibtex:

@inbook {RS-SH:16,
        Author = {Ruben Sevilla and Antonio Huerta},
        Title = {Tutorial on {H}ybridizable {D}iscontinuous {G}alerkin ({HDG}) for second-order elliptic problems},
        Editor = {J.~Schröder and P.~Wriggers},
        Booktitle = {Advanced Finite Element Technologies},
        Series = {CISM International Centre for Mechanical Sciences},
        Volume = {566},
        Publisher = {Springer International Publishing},
        Pages = {105--129},
        Year = {2016},
        Doi = {10.1007/978-3-319-31925-4_5}
        }