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Linear differential operators on bivariate spline spaces and spline vector fields

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Abstract

We consider the application of standard differentiation operators to spline spaces and spline vector fields defined on triangulations in the plane. In particular, we explore the use of Bernstein–Bézier techniques for answering questions such as: What are the images or the kernels, and their dimensions, of partial derivative, gradient, divergence, curl, or Laplace, operators. We also describe a particular continuous piecewise quadratic finite element whose nodal parameters are function and divergence (or curl) values.

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Acknowledgments

We would like to thank Noel Walkington and Alexei Kolesnikov for useful discussions, and the Towson University Fisher Foundation for supporting this project.

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Authors and Affiliations

  1. University of Utah, 155 South 1400 East, JWB 233, Salt Lake City, UT, 84112-0090, USA

    Peter Alfeld

  2. Towson University, 7800 York Road, Towson, MD, 21252, USA

    Tatyana Sorokina

Authors
  1. Peter Alfeld
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  2. Tatyana Sorokina
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Correspondence to Tatyana Sorokina.

Additional information

Communicated by Tom Lyche.

T. Sorokina is partially supported by the Simons Foundation Collaboration Grant for Mathematicians.

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Alfeld, P., Sorokina, T. Linear differential operators on bivariate spline spaces and spline vector fields. Bit Numer Math 56, 15–32 (2016). https://doi.org/10.1007/s10543-015-0557-x

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  • DOI: https://doi.org/10.1007/s10543-015-0557-x

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