TY - JOUR
T1 - Connection Between Grad-Div Stabilized Stokes Finite Elements and Divergence-Free Stokes Finite Elements
AU - Neilan , Michael
AU - Zytoon , Ahmed
JO - International Journal of Numerical Analysis and Modeling
VL - 6
SP - 839
EP - 857
PY - 2020
DA - 2020/10
SN - 17
DO - http://doi.org/
UR - https://global-sci.org/intro/article_detail/ijnam/18354.html
KW - Finite element methods, grad-div stabilization, divergence-free.
AB - <p style="text-align: justify;">In this paper, we use recently developed theories of divergence–free finite element
schemes to analyze methods for the Stokes problem with grad-div stabilization. For example, we
show that, if the polynomial degree is sufficiently large, the solutions of the Taylor–Hood finite
element scheme converges to an optimal convergence exactly divergence–free solution as the grad-div parameter tends to infinity. In addition, we introduce and analyze a stable first-order scheme
that does not exhibit locking phenomenon for large grad-div parameters.</p>