FoCM 2014 conference

Workshop A5 - Multiresolution and Adaptivity in Numerical PDEs

December 13, 17:50 ~ 18:30 - Room B23

## Instance optimality of the maximum strategy

### University of Munich (LMU), Germany   -   diening@math.lmu.de

We study the adaptive finite element approximation of the Dirichlet problem $-\Delta u = f$ with zero boundary values using newest vertex bisection. Our approach is based on the minimization of the corresponding Dirichlet energy. Our approach works for lower and higher order elements. We show that the maximums strategy attains every energy level with a number of degrees of freedom, which is proportional to the optimal number. As a consequence we achieve instance optimality of the error.

Joint work with Christian Kreuzer (Bochum, Germany) and Rob Stevenson (Amsterdam, Netherlands).