Abstract
A bivariate spline method is developed to numerically solve second order elliptic partial differential equations in non-divergence form. The existence, uniqueness, stability as well as approximation properties of the discretized solution will be established by using the well-known Ladyzhenskaya–Babuska–Brezzi condition. Bivariate splines, discontinuous splines with smoothness constraints are used to implement the method. Computational results based on splines of various degrees are presented to demonstrate the effectiveness and efficiency of our method.
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The research of Ming-Jun Lai was partially supported by Simons collaboration Grant 280646 and the National Science Foundation Award DMS-1521537. The research of Chunmei Wang was partially supported by National Science Foundation Awards DMS-1522586 and DMS-1648171.
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Lai, MJ., Wang, C. A Bivariate Spline Method for Second Order Elliptic Equations in Non-divergence Form. J Sci Comput 75, 803–829 (2018). https://doi.org/10.1007/s10915-017-0562-0
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DOI: https://doi.org/10.1007/s10915-017-0562-0