| Home > Publications > Reports > Numerical Analysis and Applied Mathematics (TW) |
TW 452
Hendrik Speleers, Paul Dierckx, and Stefan Vandewalle
Powell-Sabin splines with boundary conditions for polygonal and non-polygonal domains
Abstract
Powell-Sabin splines are piecewise quadratic polynomials with a global C1-continuity, defined on conforming triangulations. Imposing a boundary condition on such a spline leads to a set of constraints on the spline coefficients. First we discuss boundary conditions defined on a polygonal domain, before we treat boundary conditions on a general curved domain boundary. We consider Dirichlet and Neumann conditions, and we show that a particular choice of the PS-triangles at the boundary can greatly simplify the corresponding constraints. Finally, we consider an application where the techniques developped in this paper are used: the numerical solution of a partial differential equation by the Galerkin and collocation method.
report.pdf (349K) / mailto: H. Speleers