A Petrov–Galerkin method with quadrature for elliptic boundary value problems
A Petrov–Galerkin method with quadrature for elliptic boundary value problems
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DOI：
10.1093/imanum/24.1.157
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发表时间：
2004
影响因子：
2.1
通讯作者：
B. Bialecki;M. Ganesh;K. Mustapha
中科院分区：
文献类型：
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作者：
B. Bialecki;M. Ganesh;K. Mustapha
本文提出并分析了一种求解矩形区域上二阶变系数椭圆边值问题的全离散Petrov-Galerkin方法。在我们的方案中，试验空间由r ≥ 3次的C2样条构成，测试空间由r - 2次的C 0样条构成，我们使用复合（r - 1）点Gauss求积。我们证明了近似解的存在唯一性，并建立了H2，H1和L2范数下的最优阶误差界。
We propose and analyse a fully discrete Petrov-Galerkin method with quadrature, for solving second-order, variable coefficient, elliptic boundary value problems on rectangular domains. In our scheme, the trial space consists of C 2 splines of degree r ≥ 3, the test space consists of C 0 splines of degree r - 2, and we use composite (r - 1)-point Gauss quadrature. We show existence and uniqueness of the approximate solution and establish optimal order error bounds in H 2 , H 1 and L 2 norms.