The conditioning of the stiffness matrix for certain elements
approximating the incompressibility condition in fluid dynamics.
W. Dörfler
Abstract:
In order to solve the Stokes equations numerically, Crouzeix and
Raviart introduced elements satisfying a discrete divergence
condition. For the two dimensional case und uniform
triangulations it is shown that using the standard basis
functions, the conditioning of the stiffness matrix is of
order $N^2$, where $N$ is the dimension of the
corresponding finite element space. Hierarchical bases
are introduced which give a condition number of order
$N log(N)^3$.
AMS-Classification: 65F10, 65N30, 76D05
Keywords: Stokes equations, preconditioning, hierarchical bases
Appeared in: Numer. Math. 58 (1990), 203-214.
