SC 98-16 Jens Lang: Adaptive Incompressible Flow Computations with Linearly
Implicit Time Discretization and Stabilized Finite Elements (Appeared in: Computational Fluid Dynamics 98, K.D.
Papailiou, D. Tsahalis, J. Periaux, C. Hirsch, M. Pandolfi
eds., John Wiley \& Sons, New York, 1998, 200-204)
Abstract: Fully adaptive solutions of imcompressible flow problems
employing the discretization sequence first in time then in space
are presented. The time discretization is done by linearly
implicit one-step methods possibly of high order
with automatic step size control. A posteriori error estimates for the stabilized finite element discretization in
space are obtained by solving local Dirichlet problems with
higher accuracy. Once those estimates have been computed, we are able to
control time and space grids with respect to required tolerances and
necessary computational work. The devised method is applied to two benchmark
problems in 2D.
Keywords: Incompressible Flow,
Adaptive Stabilized Finite Element,
Linearly Implicit Time Discretization
MSC: 76M10