Finite Element Methods with B-Splines: Supplementary Material. The small collection of MATLAB programs illustrates the methods described in the book. Our examples show that the elegance and efficiency of B-spline algorithms, familiar from numerous applications, also prevail for the numerical solution of partial differential equations. This is due to the exceptionally simple data structure of uniform B-splines with its obvious advantages. Most importantly, regardless of the degree, the finite element subspace is spanned by translates of a single basis function, and the coefficients are associated with a regular grid; no mesh generation and connectivity data structures are necessary as for conventional finite element codes. The goal of our sample programs is not to cover a broad range of partial differential equations or to provide B-spline software ready to serve potential applications. Instead, our MATLAB routines for basic model problems are intended as examples which show how to exploit standard B-spline features. In particular, the m-files provide illustrations for teaching purposes. Moreover, experimenting with our sample codes can facilitate the development of b-spline-based finite element software. For programs and demos illustrating the geometric properties of B-splines see the supplementary material for the book Approximation and Modeling with B-Splines (OT132). . The programs of the package FEMB (Version 1.0) are test versions, intended only for educational use, and for illustrating the methods described in the SIAM book Finite Element Methods with B-Splines. No permission is granted for any other application, in particular for any commercial use or applications of the programs which can result in material or physical damage. A possible lack of reliability of the numerical algorithms, which to some extent are based on heuristic strategies, has been emphasized. As a consequence, no guarantees for the correctness of the computed results can be given. In addition to the above restrictions, the general terms of MathWorks for using MATLAB programs apply.

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References in zbMATH (referenced in 3 articles )

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  1. Apprich, Christian; Höllig, Klaus; Hörner, Jörg; Keller, Andreas; Nava Yazdani, Esfandiar: Finite element approximation with hierarchical B-splines (2015)
  2. Höllig, Klaus: Finite element methods with (B)-splines (2012) ioport
  3. Höllig, Klaus: Finite element methods with (B)-splines (2003)