We present analytical solution of the Stokes problem in 2D domains. This is then used to find the asymptotic behavior of the solution in the vicinity of corners, also for Navier-Stokes equations in 2D. We apply this to construct very precise numerical finite element solution.
@article{702891,
title = {Analytical solution of Stokes flow near corners and applications to numerical solution of Navier-Stokes equations with high precision},
booktitle = {Applications of Mathematics 2012},
series = {GDML\_Books},
publisher = {Institute of Mathematics AS CR},
address = {Prague},
year = {2012},
pages = {43-54},
mrnumber = {MR3204399},
zbl = {1313.76035},
url = {http://dml.mathdoc.fr/item/702891}
}
Burda, Pavel; Novotný, Jaroslav; Šístek, Jakub. Analytical solution of Stokes flow near corners and applications to numerical solution of Navier-Stokes equations with high precision, dans Applications of Mathematics 2012, GDML_Books, (2012), pp. 43-54. http://gdmltest.u-ga.fr/item/702891/