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On discrete maximum principles for discontinuous Galerkin methods

Author
Badia, S.; Hierro, A.
Type of activity
Journal article
Journal
Computer methods in applied mechanics and engineering
Date of publication
2015-04
Volume
286
First page
107
Last page
122
DOI
https://doi.org/10.1016/j.cma.2014.12.006 Open in new window
Repository
http://hdl.handle.net/2117/83795 Open in new window
URL
http://www.sciencedirect.com/science/article/pii/S004578251400485X Open in new window
Abstract
The aim of this work is to propose a monotonicity-preserving method for discontinuous Galerkin (dG) approximations of convection–diffusion problems. To do so, a novel definition of discrete maximum principle (DMP) is proposed using the discrete variational setting of the problem, and we show that the fulfilment of this DMP implies that the minimum/maximum (depending on the sign of the forcing term) is on the boundary for multidimensional problems. Then, an artificial viscosity (AV) technique i...
Citation
Badia, S., Hierro, A. On discrete maximum principles for discontinuous Galerkin methods. "Computer methods in applied mechanics and engineering", Abril 2015, vol. 286, p. 107-122.
Keywords
Convection-dominated flows, Convection–diffusion, Discontinuous Galerkin, Nonlinear stabilization, Shock capturing, Stabilized finite elements
Group of research
(MC)2 - UPC Computational continuum mechanics
ANiComp - Numerical analysis and scientific computation

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