New shape functions for triangular p-FEM using integrated Jacobi polynomials
New shape functions for triangular p-FEM using integrated Jacobi polynomials
复制标题
DOI：
10.1007/s00211-006-0681-2
复制
发表时间：
2006-05
影响因子：
2.1
通讯作者：
S. Beuchler;J. Schöberl
中科院分区：
文献类型：
--
作者：
S. Beuchler;J. Schöberl
本文用三角网格上的分段多项式函数对二阶边值问题−∇·((x，y)∇u)=f进行了有限元离散。在参考元素上，我们将积分雅可比多项式定义为内部ansatz函数。如果是每个三角形上的常值函数，且每个三角形都有直边，我们证明了单元刚度矩阵的非零矩阵项不多。给出了预条件的一个应用。数值算例表明了该方法的优越性。
In this paper, the second order boundary value problem −∇·( (x,y)∇u)=fis discretized by the Finite Element Method using piecewise polynomial functions of degreepon a triangular mesh. On the reference element, we define integrated Jacobi polynomials as interior ansatz functions. If is a constant function on each triangle and each triangle has straight edges, we prove that the element stiffness matrix has not more than nonzero matrix entries. An application for preconditioning is given. Numerical examples show the advantages of the proposed basis.