A Bivariate Spline Method for Second Order Elliptic Equations in Non-Divergence Form
Numerical Analysis
2017-01-05 v2
Abstract
A bivariate spline method is developed to numerically solve second order elliptic partial differential equations (PDE) 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 (LBB) condition. Bivariate splines, discontinuous splines with smoothness constraints are used to implement the method. A plenty of computational results based on splines of various degrees are presented to demonstrate the effectiveness and efficiency of our method.
Cite
@article{arxiv.1610.05746,
title = {A Bivariate Spline Method for Second Order Elliptic Equations in Non-Divergence Form},
author = {Ming-Jun Lai and Chunmei Wang},
journal= {arXiv preprint arXiv:1610.05746},
year = {2017}
}
Comments
23 pages, 20 table, 1 figure