TY - JOUR
T1 - Streamline Diffusion Virtual Element Method for Convection-Dominated Diffusion Problems
AU - Li , Yuxia
AU - Xie , Cong
AU - Feng , Xinglong
JO - East Asian Journal on Applied Mathematics
VL - 1
SP - 158
EP - 180
PY - 2020
DA - 2020/01
SN - 10
DO - http://doi.org/10.4208/eajam.231118.240619
UR - https://global-sci.org/intro/article_detail/eajam/13608.html
KW - Convection dominated diffusion problem, streamline diffusion virtual element method,
stabilisation, optimal convergence, boundary layer problem.
AB - <p style="text-align: justify;">A novel streamline diffusion form of virtual element method for convection-dominated diffusion problems is studied. The main feature of the method is that the test function in the stabilised term has the adjoint operator-like form (−∇·($K$(<strong>x</strong>)∇$v$)<span style="text-align: justify;">−</span><strong>b</strong>(<strong>x</strong>)·∇$v$). Unlike the standard VEM, the stabilisation scheme can efficiently avoid nonphysical oscillations. The well-posedness of the problem is also proven and error estimates are provided. Numerical examples show the stability of the method for very large Péclet numbers and its applicability to boundary layer problem.</p>