Journal of Scientific Computing

, Volume 75, Issue 2, pp 803–829 | Cite as

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

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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.

Keywords

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

Mathematics Subject Classification

65N30 65N12 35J15 35D35 

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Copyright information

© Springer Science+Business Media, LLC 2017

Authors and Affiliations

  1. 1.Department of MathematicsUniversity of GeorgiaAthensUSA
  2. 2.Department of MathematicsTexas State UniversitySan MarcosUSA

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