Thomas Takacs: Smooth isogeometric discretizations for fourth order PDEs

Standard Galerkin discretizations of fourth order partial differential equations require discretization spaces that are at least \(H^2\)-conforming. In this talk we focus on planar and surfaces domains and consider isogeometric discretizations, that is, spline based discretizations over domains parameterized by spline mappings. As a consequence of the regularity condition, the discretization spaces must be at least \(C^1\)-smooth. We study how this regularity condition relates to concepts of smoothness in computer-aided geometric design. We discuss several approaches to construct smooth surfaces and compare their properties, both from a geometric design and a numerical analysis perspective.