Projection methods for Dirichlet’s problem in approximating polygonal domains with boundary-value corrections
Projection methods for Dirichlet’s problem in approximating polygonal domains with boundary-value corrections
复制标题
带边界值修正的近似多边形域狄利克雷问题的投影方法
DOI：
10.1090/s0025-5718-1972-0343657-7
复制
发表时间：
1972
影响因子：
2
通讯作者：
V. Thomée
中科院分区：
文献类型：
--
作者：
J. Bramble;T. Dupont;V. Thomée
考虑狄利克雷问题在平面域与光滑边界aQ。问其近似解的目的,一个近似域心不在焉,0 < h与多边形边界aQh _ 1,介绍aQh段的长度最多h。一个由Nitsche引入投影法(6)然后Qh给出一个近似解应用于上海有限维子空间的功能,例如空间样条函数上定义Q2h的三角测量。与Nitsche方法相关的双线性形式的边界项被修改以校正边界的摄动。
Consider Dirichlet's problem in a plane domain Q with smooth boundary aQ. For the purpose of its approximate solution, an approximating domain Qh, 0 < h _ 1, with polygonal boundary aQh iS introduced where the segments of aQh have length at most h. A projection method introduced by Nitsche (6) is then applied on Qh to give an approximate solution in a finite-dimensional subspace of functions Sh, for instance a space of splines defined on a triangulation of Q2h. The boundary terms in the bilinear form associated with Nitsche's method are modified to correct for the perturbation of the boundary.