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 -

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.