Group Seminar: Group Geometry in Simulations
Date: Thursday May 2, 2024
Time and location: 10:15 am, S4 025
Abstract: In this talk we discuss an isogeometric mortar method for fourth order elliptic problems. In particular we are interested in the discretization of the biharmonic equation on multi-patch domains. The domain is partitioned into patches that are parametrized by tensor-product B-spline mappings. The patch parametrizations are C^0-conforming. We exploit the mortar technique to weakly enforce C^1-continuity across the patch interfaces. In order to obtain discrete inf-sup stability, a particular choice for the Lagrange multiplier space is needed. To be precise, we use as a multiplier space splines of degree reduced by two, w.r.t. the degree of the primal spline space, and with increased smoothness near all patch corners. In this framework, we are able to show optimal a priori error estimates. We also perform numerical tests to validate the theoretical results.
This talk is based on joint work with Andrea Benvenuti, Gabriele Loli (both Universita di Pavia, IT) and Giancarlo Sangalli (Universita di Pavia \& IMATI- CNR, Pavia, IT).