TY - JOUR
T1 - A Bivariate Spline Method for Second Order Elliptic Equations in Non-divergence Form
AU - Lai, Ming Jun
AU - Wang, Chunmei
N1 - Funding Information:
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.
Publisher Copyright:
© 2017, Springer Science+Business Media, LLC.
PY - 2018/5/1
Y1 - 2018/5/1
N2 - 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.
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.
KW - Cordes condition
KW - Discontinuous Galerkin
KW - Finite element methods
KW - Primal-dual
KW - Spline approximation
UR - http://www.scopus.com/inward/record.url?scp=85029602891&partnerID=8YFLogxK
U2 - 10.1007/s10915-017-0562-0
DO - 10.1007/s10915-017-0562-0
M3 - Article
AN - SCOPUS:85029602891
VL - 75
SP - 803
EP - 829
JO - Journal of Scientific Computing
JF - Journal of Scientific Computing
SN - 0885-7474
IS - 2
ER -