A Bivariate Spline Method for Second Order Elliptic Equations in Non-divergence Form

Ming Jun Lai, Chunmei Wang

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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.

Original languageEnglish
Pages (from-to)803-829
Number of pages27
JournalJournal of Scientific Computing
Issue number2
StatePublished - May 1 2018



  • Cordes condition
  • Discontinuous Galerkin
  • Finite element methods
  • Primal-dual
  • Spline approximation

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