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A Polygonal Spline Method for General Second-Order Elliptic Equations and Its Applications

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Approximation Theory XV: San Antonio 2016 (AT 2016)

Part of the book series: Springer Proceedings in Mathematics & Statistics ((PROMS,volume 201))

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Abstract

We explain how to use polygonal splines to numerically solve second-order elliptic partial differential equations. The convergence of the polygonal spline method will be studied. Also, we will use this approach to numerically study the solution of some mixed parabolic and hyperbolic partial differential equations. Comparison with standard bivariate spline method will be given to demonstrate that our polygonal splines have some better numerical performance.

This research is partially supported by Simons Collaboration Grant 280646 and the National Science Foundation under the Grant #DMS 1521537.

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Authors and Affiliations

  1. Department of Mathematics, University of Georgia, Athens, GA, 30602, USA

    Ming-Jun Lai & James Lanterman

Authors
  1. Ming-Jun Lai
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  2. James Lanterman
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Correspondence to Ming-Jun Lai .

Editor information

Editors and Affiliations

  1. Department of Applied Mathematics and Statistics, Colorado School of Mines, Golden, Colorado, USA

    Gregory E. Fasshauer

  2. Department of Mathematics, Vanderbilt University , Nashville, Tennessee, USA

    Larry L. Schumaker

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Lai, MJ., Lanterman, J. (2017). A Polygonal Spline Method for General Second-Order Elliptic Equations and Its Applications. In: Fasshauer, G., Schumaker, L. (eds) Approximation Theory XV: San Antonio 2016. AT 2016. Springer Proceedings in Mathematics & Statistics, vol 201. Springer, Cham. https://doi.org/10.1007/978-3-319-59912-0_6

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