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Volume 35, Issue 5
On the Discrete Maximum Principle for the Local Projection Scheme with Shock Capturing

Piotr Skrzypacz & Dongming Wei

DOI: 10.4208/jcm.1605-m2015-0479

J. Comp. Math., 35 (2017), pp. 547-568.

Published online: 2017-10

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  • Abstract

It is a well known fact that finite element solutions of convection dominated problems can exhibit spurious oscillations in the vicinity of boundary layers. One way to overcome this numerical instability is to use schemes that satisfy the discrete maximum principle. There are monotone methods for piecewise linear elements on simplices based on the upwind techniques or artificial diffusion. In order to satisfy the discrete maximum principle for the local projection scheme, we add an edge oriented shock capturing term to the bilinear form. The analysis of the proposed stabilisation method is complemented with numerical examples in 2D.

  • Keywords

Local projection stabilization, Discrete maximum principle, Shock capturing.

  • AMS Subject Headings

65N30, 65M60.

  • Copyright

COPYRIGHT: © Global Science Press

  • Email address

piotr.skrzypacz@nu.edu.kz (Piotr Skrzypacz)

dongming.wei@nu.edu.kz (Dongming Wei)

  • BibTex
  • RIS
  • TXT
@Article{JCM-35-547, author = {Skrzypacz , Piotr and Wei , Dongming}, title = {On the Discrete Maximum Principle for the Local Projection Scheme with Shock Capturing}, journal = {Journal of Computational Mathematics}, year = {2017}, volume = {35}, number = {5}, pages = {547--568}, abstract = {

It is a well known fact that finite element solutions of convection dominated problems can exhibit spurious oscillations in the vicinity of boundary layers. One way to overcome this numerical instability is to use schemes that satisfy the discrete maximum principle. There are monotone methods for piecewise linear elements on simplices based on the upwind techniques or artificial diffusion. In order to satisfy the discrete maximum principle for the local projection scheme, we add an edge oriented shock capturing term to the bilinear form. The analysis of the proposed stabilisation method is complemented with numerical examples in 2D.

}, issn = {1991-7139}, doi = {https://doi.org/10.4208/jcm.1605-m2015-0479}, url = {http://global-sci.org/intro/article_detail/jcm/10031.html} }
TY - JOUR T1 - On the Discrete Maximum Principle for the Local Projection Scheme with Shock Capturing AU - Skrzypacz , Piotr AU - Wei , Dongming JO - Journal of Computational Mathematics VL - 5 SP - 547 EP - 568 PY - 2017 DA - 2017/10 SN - 35 DO - http://doi.org/10.4208/jcm.1605-m2015-0479 UR - https://global-sci.org/intro/article_detail/jcm/10031.html KW - Local projection stabilization, Discrete maximum principle, Shock capturing. AB -

It is a well known fact that finite element solutions of convection dominated problems can exhibit spurious oscillations in the vicinity of boundary layers. One way to overcome this numerical instability is to use schemes that satisfy the discrete maximum principle. There are monotone methods for piecewise linear elements on simplices based on the upwind techniques or artificial diffusion. In order to satisfy the discrete maximum principle for the local projection scheme, we add an edge oriented shock capturing term to the bilinear form. The analysis of the proposed stabilisation method is complemented with numerical examples in 2D.

PiotrSkrzypacz & DongmingWei. (2020). On the Discrete Maximum Principle for the Local Projection Scheme with Shock Capturing. Journal of Computational Mathematics. 35 (5). 547-568. doi:10.4208/jcm.1605-m2015-0479
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