Powell–Sabin splines with boundary conditions for polygonal and non-polygonal domains
نویسندگان
چکیده
Powell–Sabin splines are piecewise quadratic polynomials with a global C1-continuity, defined on conforming triangulations. Imposing boundary conditions 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 developed in this paper are used: the numerical solution of a partial differential equation by the Galerkin and collocation method. © 2006 Elsevier B.V. All rights reserved.
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