Seminar in the framework of the PDE Afternoon

Type seminar
Time 16:00 - 16:30
Place Vienna University of Technology, Wiedner Hauptstraße 8, Vienna (map)
Room Seminarraum DA Grün 03B
Speaker Gregor Gantner (Vienna University of Technology)
Title Optimal Adaptivity for Splines in Finite and Boundary Element Methods
Abstract The CAD standard for geometry representation in 2D or 3D relies on tensor-product splines. Isogeometric analysis (IGA) uses the same splines for the ansatz space as for the geometry. To allow for adaptive refinement, several extensions have emerged, e.g., analysis-suitable T-splines, hierarchical splines, or LR-splines. All these concepts have been studied via numerical experiments. However, so far there exists only little literature concerning the thorough mathematical analysis of adaptive isogeometric finite and boundary element methods (IGAFEM/IGABEM). For standard FEM and BEM with piecewise polynomials, adaptivity is well understood. In this talk, we consider an IGAFEM/IGABEM for elliptic (possibly non-symmetric) second-order PDEs in arbitrary space dimension. We employ hierarchical splines of arbitrary degree. We propose an adaptive algorithm which guarantees linear convergence of the error estimator with optimal algebraic rate.