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Numerical solution of partial differential equations with Powell–Sabin splines by Hendrik Speleers; Paul Dierckx; Stefan Vandewalle is a Mathematics article available to read on EtoBox.

What is Numerical solution of partial differential equations with Powell–Sabin splines about?

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.

Who reads Numerical solution of partial differential equations with Powell–Sabin splines?

Author

Hendrik Speleers; Paul Dierckx; Stefan Vandewalle

Publisher

Elsevier Science; Elsevier ; Elsevier BV (ISSN 0377-0427)

Published

2006

Language

EN

Field

Mathematics (Physical Sciences)