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Journal of Computational Mathematics 2017, Vol. 35 Issue (5) :547-568    DOI: 10.4208/jcm.1605-m2015-0479
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ON THE DISCRETE MAXIMUM PRINCIPLE FOR THE LOCAL PROJECTION SCHEME WITH SHOCK CAPTURING
Piotr Skrzypacz, Dongming Wei
Nazarbayev University, School of Science and Technology, 53 Kabanbay Batyr Ave., Astana 010000 Kazakhstan

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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.
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MSC2000:

65N30;65M60

;
KeywordsLocal projection stabilization   Discrete maximum principle   Shock capturing     
Received: 2015-12-18;
Cite this article:   
.ON THE DISCRETE MAXIMUM PRINCIPLE FOR THE LOCAL PROJECTION SCHEME WITH SHOCK CAPTURING[J]  Journal of Computational Mathematics, 2017,V35(5): 547-568
URL:  
http://123.57.41.99/Jwk_jcm/EN/10.4208/jcm.1605-m2015-0479      OR     http://123.57.41.99/Jwk_jcm/EN/Y2017/V35/I5/547
 
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