Triangular Berstein-Be´zier patches
Computer Aided Geometric Design
Multivariate vertex splines and finite elements
Journal of Approximation Theory
Hierarchical conforming finite element methods for the biharmonic equation
SIAM Journal on Numerical Analysis
Curve and surface fitting with splines
Curve and surface fitting with splines
Surface fitting using convex Powell-Sabin splines
Journal of Computational and Applied Mathematics
On calculating normalized Powell-Sabin B-splines
Computer Aided Geometric Design
Piecewise Quadratic Approximations on Triangles
ACM Transactions on Mathematical Software (TOMS)
Finite Element Method for Elliptic Problems
Finite Element Method for Elliptic Problems
Uniform Powell--Sabin spline wavelets
Journal of Computational and Applied Mathematics
Local subdivision of Powell-Sabin splines
Computer Aided Geometric Design
Powell-Sabin splines with boundary conditions for polygonal and non-polygonal domains
Journal of Computational and Applied Mathematics
Quasi-hierarchical Powell--Sabin B-splines
Computer Aided Geometric Design
A normalized basis for quintic Powell--Sabin splines
Computer Aided Geometric Design
A normalized basis for reduced Clough-Tocher splines
Computer Aided Geometric Design
Hi-index | 7.29 |
Powell-Sabin splines are piecewise quadratic polynomials with global C^1-continuity. They are defined on conforming triangulations of two-dimensional domains, and admit a compact representation in a normalized B-spline basis. Recently, these splines have been used successfully in the area of computer-aided geometric design for the modelling and fitting of surfaces. In this paper, we discuss the applicability of Powell-Sabin splines for the numerical solution of partial differential equations defined on domains with polygonal boundary. A Galerkin-type PDE discretization is derived for the variable coefficient diffusion equation. Special emphasis goes to the treatment of Dirichlet and Neumann boundary conditions. Finally, an error estimator is developed and an adaptive mesh refinement strategy is proposed. We illustrate the effectiveness of the approach by means of some numerical experiments.