#### Conference abstracts

Session B6 - Multiresolution and Adaptivity in Numerical PDEs

July 14, 15:30 ~ 15:55

## On the error control for fully discrete approximations of the time-dependent Stokes equation.

### University of Chester, UK   -   f.karakatsani@chester.ac.uk

We consider fully discrete finite element approximations to the time-dependent Stokes system. The space discretization is based on popular stable spaces, including Crouzeix-Raviart and Taylor-Hood finite element methods. Implicit Euler is applied for the time discretization. The finite element spaces are allowed to change with time steps and the projection steps include alternatives that are hoped to cope with possible numerical artifices and the loss of the discrete incompressibility of the schemes. The final estimates are of optimal order in $L^\infty (L^2)$ for the velocity error.

Joint work with Eberhard B\"ansch (University of Erlangen, Germany), Charalambos Makridakis (University of Sussex, UK).

FoCM 2017, based on a nodethirtythree design.