For more information about this meeting, contact Yuxi Zheng, Kris Jenssen.

Title: | On the convergence properties of the Generalized Finite Element Method |

Seminar: | CCMA PDEs and Numerical Methods Seminar Series |

Speaker: | Cosmin Anitescu, Syracuse University |

Abstract: |

The Generalized Finite Element Method (GFEM) is an extension of the standard finite element method, which uses a partition of unity and
local approximation spaces. In some cases, the partition of unity functions may have some approximation properties themselves (for example, "hat"
partition of unity functions reproduce all piecewise linears). More generally, suppose that the partition of unity functions reproduce polynomials
of degree l. Then if the local approximation spaces contain polynomials of degree k, it will be shown that for a smooth exact solution, the error of
the GFEM approximation is of the order O(h^{k+l}) in H^1 norm. This result could not be obtained from the classical error estimate of GFEM, which
does not reflect the approximation properties of the partition of unity functions. Some results on the superconvergence of GFEM, with reference to
the behavior near the boundary of the domain, will also be presented as time allows. Host: Victor Nistor |

### Room Reservation Information

Room Number: | MB216 |

Date: | 01 / 18 / 2010 |

Time: | 03:35pm - 04:25pm |