TY - JOUR
T1 - Adaptive $H$(div)-Conforming Embedded-Hybridized Discontinuous Galerkin Finite Element Methods for the Stokes Problems
AU - Han , Yihui
AU - Leng , Haitao
JO - CSIAM Transactions on Applied Mathematics
VL - 1
SP - 82
EP - 108
PY - 2022
DA - 2022/03
SN - 3
DO - http://doi.org/10.4208/csiam-am.SO-2021-0023
UR - https://global-sci.org/intro/article_detail/csiam-am/20289.html
KW - Stokes equations, HDG methods, E-HDG methods, a posteriori error estimator, divergence-free, $H$(div)-conforming.
AB - <p style="text-align: justify;">In this paper, we propose a residual-based a posteriori error estimator of
embedded–hybridized discontinuous Galerkin finite element methods for the Stokes
problems in two and three dimensions. The piecewise polynomials of degree $k (k≥1)$ and $k−1$ are used to approximate the velocity and pressure in the interior of elements, and the piecewise polynomials of degree $k$ are utilized to approximate the velocity and pressure on the inter-element boundaries. The attractive properties, named
divergence-free and $H$(div)-conforming, are satisfied by the approximate velocity field.
We prove that the a posteriori error estimator is robust in the sense that the ratio of the
upper and lower bounds is independent of the mesh size and the viscosity. Finally, we
provide several numerical examples to verify the theoretical results.</p>