On discrete maximum principles for discontinuous Galerkin methods

Santiago Badia, Alba Hierro

Research output: Contribution to journalArticleResearchpeer-review

13 Citations (Scopus)

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 is designed for convection-dominant problems that satisfies the above mentioned DMP. The noncomplete stabilized interior penalty dG method is proved to fulfil the DMP property for the one-dimensional linear case when adding such AV with certain parameters. The benchmarks for the constant values to satisfy the DMP are calculated and tested in the numerical experiments section. Finally, the method is applied to different test problems in one and two dimensions to show its performance.

Original languageEnglish
Pages (from-to)107-122
Number of pages16
JournalComputer Methods in Applied Mechanics and Engineering
Volume286
DOIs
Publication statusPublished - 1 Apr 2015
Externally publishedYes

Keywords

  • Convection-diffusion
  • Convection-dominated flows
  • Discontinuous galerkin
  • Nonlinear stabilization
  • Shock capturing
  • Stabilized finite elements

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