New shape functions for triangular p-FEM using integrated Jacobi polynomials

被引：44

作者：

Beuchler, S

Schoeberl, J

机构：

[1] Johannes Kepler Univ Linz, Inst Computat Math, A-4040 Linz, Austria

[2] Austrian Acad Sci, Johann Radon Inst Computat & Appl Math, A-4040 Linz, Austria

来源：

NUMERISCHE MATHEMATIK | 2006年 / 103卷 / 03期

关键词：

D O I：

10.1007/s00211-006-0681-2

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

In this paper, the second order boundary value problem -del center dot (A(x,y) del u)=f is discretized by the Finite Element Method using piecewise polynomial functions of degree p on a triangular mesh. On the reference element, we define integrated Jacobi polynomials as interior ansatz functions. If A is a constant function on each triangle and each triangle has straight edges, we prove that the element stiffness matrix has not more than 25/2 p(2) nonzero matrix entries. An application for preconditioning is given. Numerical examples show the advantages of the proposed basis.

引用

页码：339 / 366

页数：28