This paper deals with an extension of one-dimensional Clenshaw-Curtis quadrature rule to Rd, d ≥ 2 on a convex domain. As one of its applications, we apply this quadrature rule to a collocation least-squares method using arbitrary abscissas for a first-order system of an elliptic boundary value problem so that the convergence analysis on a numerical solution can be shown in a standard Sobolev norm.
Bibliographical noteFunding Information:
The second author is supported by the grant KRF-2005-070-C00017 and the third author is also supported by the grant R01-2006-000-10424-0 from Korea Science and Engineering Foundation in Ministry of Science & Technology.
- Clenshaw-Curtis quadrature rule
- Collocation least-squares methods
- First-order system