TY - JOUR
T1 - Adaptive Virtual Element Method for Convection Dominated Diffusion Equations
AU - Wang , Qiming
AU - Zhou , Zhaojie
JO - Journal of Computational Mathematics
VL - 1
SP - 174
EP - 202
PY - 2024
DA - 2024/11
SN - 43
DO - http://doi.org/10.4208/jcm.2309-m2021-0366
UR - https://global-sci.org/intro/article_detail/jcm/23534.html
KW - A posteriori estimate, SUPG virtual element method, Convection dominated
diffusion equation, Adaptive VEM algorithm.
AB - <p style="text-align: justify;">In this paper, a robust residual-based a posteriori estimate is discussed for the Streamline Upwind/Petrov Galerkin (SUPG) virtual element method (VEM) discretization of
convection dominated diffusion equation. A global upper bound and a local lower bound
for the a posteriori error estimates are derived in the natural SUPG norm, where the global
upper estimate relies on some hypotheses about the interpolation errors and SUPG virtual
element discretization errors. Based on the Dörfler’s marking strategy, adaptive VEM algorithm drived by the error estimators is used to solve the problem on general polygonal
meshes. Numerical experiments show the robustness of the a posteriori error estimates.</p>