Convergence analysis of a finite element method for second order non-variational elliptic problems

被引:6
作者
Neilan, Michael [1 ]
机构
[1] Univ Pittsburgh, Math, 139 Univ Pl 301 Thackeray Hall, Pittsburgh, PA 15215 USA
基金
美国国家科学基金会;
关键词
non-divergence form; finite element methods; mixed methods; convergence analysis;
D O I
10.1515/jnma-2016-1017
中图分类号
O29 [应用数学];
学科分类号
070104 ;
摘要
We introduce and analyze a family of finite element methods for elliptic partial differential equations in non-variational form with non-differentiable coefficients. The finite element method studied is a variant of the one recently proposed in [Lakkis & Pryer, SIAM J. Sci. Comput., 2011], where a finite element Hessian is introduced as an auxiliary unknown. We modify the definition of the finite element Hessian rendering the auxiliary variable completely local, thus resulting in a more efficient scheme. We show that the method is stable under general conditions on the coefficient matrix and derive error estimates in a discrete H-2-norm provided the discretization parameter is sufficiently small. Numerical experiments are presented which verify the theoretical results.
引用
收藏
页码:169 / 184
页数:16
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