Abstract
Weighted and isogeometric methods use b-splines to construct bases for FEM. They combine the computational efficiency of regular grids with the geometric flexibility of CAD representations. We give a brief description of the key ideas of the two approaches, presenting them in a unified framework. In particular, we use b-spline nodes, to visualize the free parameters. Moreover, we explain how to combine features of both techniques by introducing weighted isogeometric finite elements. An error estimate for the resulting mixed method is given, and the performance of weighted approximations is illustrated by numerical examples.
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Höllig, K., Hörner, J., Hoffacker, A. (2012). Finite Element Analysis with B-Splines: Weighted and Isogeometric Methods. In: Boissonnat, JD., et al. Curves and Surfaces. Curves and Surfaces 2010. Lecture Notes in Computer Science, vol 6920. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-27413-8_21
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DOI: https://doi.org/10.1007/978-3-642-27413-8_21
Publisher Name: Springer, Berlin, Heidelberg
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