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Local Approximation from Spline Spaces on Box Meshes

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Abstract

This paper analyzes the approximation properties of spaces of piecewise tensor product polynomials over box meshes with a focus on application to isogeometric analysis. Local and global error bounds with respect to Sobolev or reduced seminorms are provided. Attention is also paid to the dependence on the degree, and exponential convergence is proved for the approximation of analytic functions in the absence of non-convex extended supports.

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Notes

  1. All the assumptions are conveniently listed in Table 1.

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Acknowledgements

The first author has received funding from the European Research Council under the European Union’s Seventh Framework Programme (FP7/2007-2013)/ERC Grant Agreement 339643.

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Authors and Affiliations

  1. Department of Mathematics, University of Pavia, via Ferrata 5, 27100, Pavia, Italy

    Andrea Bressan

  2. Department of Mathematics, University of Oslo, P.O. Box 1053, 0316, Blindern, Oslo, Norway

    Tom Lyche

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Correspondence to Andrea Bressan.

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Bressan, A., Lyche, T. Local Approximation from Spline Spaces on Box Meshes. Found Comput Math 21, 807–848 (2021). https://doi.org/10.1007/s10208-020-09467-8

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