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

Ming Jun Lai; Chunmei Wang

doi:10.1007/s10915-017-0562-0

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

Ming Jun Lai, Chunmei Wang

Mathematics and Statistics

Research output: Contribution to journal › Article › peer-review

1 Scopus citations

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.

Original language	English
Pages (from-to)	803-829
Number of pages	27
Journal	Journal of Scientific Computing
Volume	75
Issue number	2
DOIs	https://doi.org/10.1007/s10915-017-0562-0
State	Published - May 1 2018

Keywords

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

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10.1007/s10915-017-0562-0

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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.",

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AB - 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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KW - Finite element methods

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