HDGlab: An open-source implementation of the hybridisable discontinuous Galerkin method in MATLAB

Author (s): Giacomini, M.; Sevilla, R. and Huerta, A.
Journal: Archives of Computational Methods in Engineering

Volume: 28, Issue 3
Pages: 1941 – 1986
Date: 2021

Abstract:
This paper presents HDGlab, an open source MATLAB implementation of the hybridisable discontinuous Galerkin (HDG) method. The main goal is to provide a detailed description of both the HDG method for elliptic problems and its implementation available in HDGlab. Ultimately, this is expected to make this relatively new advanced discretisation method more accessible to the computational engineering community. HDGlab presents some features not available in other implementations of the HDG method that can be found in the free domain. First, it implements high-order polynomial shape functions up to degree nine, with both equally-spaced and Fekete nodal distributions. Second, it supports curved isoparametric simplicial elements in two and three dimensions. Third, it supports non-uniform degree polynomial approximations and it provides a flexible structure to devise degree adaptivity strategies. Finally, an interface with the open-source high-order mesh generator Gmsh is provided to facilitate its application to practical engineering problems.

Code repository: https://git.lacan.upc.edu/hybridLab/HDGlab

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Bibtex:

@article{HDGlab-GSH-21,
        author = {Matteo Giacomini and Ruben Sevilla and Antonio Huerta},
        title = {{HDGlab}: {A}n open-source implementation of the hybridisable 
		 discontinuous {G}alerkin method in {MATLAB}},
        fjournal = {Archives of Computational Methods in Engineering},
        journal = {Arch. Comput. Methods Eng.},
        volume = {28},
	number = {3},
        pages = {1941--1986},
        year = {2021},
	doi = {10.1007/s11831-020-09502-5}
}