### Mathematics Colloquium

# Oleg Davydov

### (Giessen)

## "Approximation by anisotropic piecewise polynomials"

** Date: ** |
Mon, September 22, 2014 |

** Time: ** |
17:15 |

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

**Abstract:** We discuss the optimal order of approximation of smooth functions by piecewise polynomials on partitions with convex cells. It turns out that appropriate anisotropic partitions allow the order O(N^{-2/(d+1)}) of piecewise constant approximation, where d>=2 is the number of variables and N is the number of cells of the partition. This is significantly better than the order O(N^{-1/d}) obtainable on isotropic partitions. For higher polynomial degrees similar improvements are achieved if the function is approximated by a sum of piecewise polynomials over a number of overlaying convex partitions.