期刊
JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS
卷 189, 期 1-2, 页码 643-659出版社
ELSEVIER SCIENCE BV
DOI: 10.1016/j.cam.2005.03.001
关键词
spline functions; finite elements; adaptive mesh refinement
Powell-Sabin splines are piecewise quadratic polynomials with global C-1-continuity. They are defined on con-forming 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. (c) 2005 Elsevier B.V. All rights reserved.
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