FESTUNG: A MATLAB/GNU Octave toolbox for the discontinuous Galerkin method, Part I: Diffusion operator

This is the first in a series of papers on implementing a discontinuous Galerkin (DG) method as an open source MATLAB/GNU Octave toolbox. The intention of this ongoing project is to provide a rapid prototyping package for application development using DG methods. The implementation relies on fully vectorized matrix/vector operations and is carefully documented; in addition, a direct mapping between discretization terms and code routines is maintained throughout. The present work focuses on a two-dimensional time-dependent diffusion equation with space/time-varying coefficients. The spatial discretization is based on the local discontinuous Galerkin formulation. Approximations of orders zero through four based on orthogonal polynomials have been implemented; more spaces of arbitrary type and order can be easily accommodated by the code structure.