@Article{CSIAM-AM-3-82, author = {Yihui and Han and and 22463 and and Yihui Han and Haitao and Leng and and 22464 and and Haitao Leng}, title = {Adaptive $H$(div)-Conforming Embedded-Hybridized Discontinuous Galerkin Finite Element Methods for the Stokes Problems}, journal = {CSIAM Transactions on Applied Mathematics}, year = {2022}, volume = {3}, number = {1}, pages = {82--108}, abstract = {

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.

}, issn = {2708-0579}, doi = {https://doi.org/10.4208/csiam-am.SO-2021-0023}, url = {http://global-sci.org/intro/article_detail/csiam-am/20289.html} }