### Mathematics Colloquium

# Lars Diening

### (Universität Osnabrück)

## "Adaptive finite element method and the maximum strategy"

** Date: ** |
Mon, November 23, 2015 |

** Time: ** |
17:15 |

** Place: ** |
Research II Lecture Hall |

**Abstract:** We study finite element solutions of the Dirichlet problem \(-\Delta u= f\) with zero boundary values. For the discrete solution the domain is usually decomposed into triangles and only the values at the nodes are calculated. To achieve high accuracy at low cost, it is desirable to have smaller triangles, only where the solution has singularities. This reduces the size of the related linear equations considerably. The adaptive finite element methods uses so called error indicators to automatically refine the triangles, where it is necessary. The "maximum strategy" is a kind of greedy algorithm that only refines those triangles, where the error indicator is maximal. We show that the relation between accuracy and number of triangles needed for this accuracy is optimal for the "maximum strategy". In particular, the method produces triangulations of minimal size.

*The colloquium is preceded by tea from 16:45 in the Resnikoff Mathematics Common Room, Research I, 127.*