FESTUNG: A MATLAB/GNU Octave toolbox for the discontinuous Galerkin method, Part II: Advection operator and slope limiting. (October 2016)

• Record Type: Journal Article
• Authors: Reuter, Balthasar; Aizinger, Vadym; Wieland, Manuel; Frank, Florian; Knabner, Peter
• Is Part Of: Computers & mathematics with applications. Volume 72:issue 7(2016)
• Page Start: 1896
• Page End: 1925
• Publication Date: 2016-10
• Subjects: Matlab/GNU Octave -- Discontinuous Galerkin method -- Slope limiting -- Vectorization -- Open source -- Advection operator; Electronic data processing -- Periodicals; Mathematics -- Data processing -- Periodicals; 510.28541
• DOI: 10.1016/j.camwa.2016.08.006
• Languages: English
• ISSNs: 0898-1221

Abstract

Abstract: This is the second 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 offer a rapid prototyping package for application development using DG methods. The implementation relies on fully vectorized matrix/vector operations and is comprehensively documented. Particular attention was paid to maintaining a direct mapping between discretization terms and code routines as well as to supporting the full code functionality in GNU Octave. The present work focuses on a two-dimensional time-dependent linear advection equation with space/time-varying coefficients, and provides a general order implementation of several slope limiting schemes for the DG method.