A priori error estimates of finite element solutions of parametrized strongly nonlinear boundary value problems
A priori error estimates of finite element solutions of parametrized strongly nonlinear boundary value problems
复制标题
参数化强非线性边值问题有限元解的先验误差估计
DOI：
10.1016/s0377-0427(96)00149-5
复制
发表时间：
1997
影响因子：
2.4
通讯作者：
I. Babuska
中科院分区：
文献类型：
--
作者：
T. Tsuchiya;I. Babuska
带参数的非线性边值问题称为参数化非线性边值问题。研究一维有界区间上二阶参数化强非线性散度型边值问题有限元解的先验误差估计。在误差分析的公式中选择了Banach空间W_（01，∞），使得由微分方程定义的非线性微分算子是指数为1的非线性Fredholm算子。有限元解决方案的定义在一个自然的方式，并证明了几个先验估计定期分支和分支周围的转折点。在证明中，Brezzi等人（1980）的扩展隐函数定理起着重要作用。
Nonlinear boundary value problems with parameters are called parametrized nonlinear boundary problems. This paper studies a priori error estimates of finite element solutions of second-order parametrized strongly nonlinear boundary value problems in divergence form on one-dimensional bounded intervals. The Banach space W01, ∞is chosen in formulation of the error analysis so that the nonlinear differential operators defined by the differential equations are nonlinear Fredholm operators of index 1. Finite element solutions are defined in a natural way, and several a priori estimates are proved on regular branches and on branches around turning points. In the proofs the extended implicit function theorem due to Brezzi et al. (1980) plays an essential role.
DOI：
10.1007/978-3-662-00547-7
发表时间：
1985
期刊：
--
影响因子：
--
作者：
K. Deimling
通讯作者：
K. Deimling