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 - <p style="text-align: justify;">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.</p>