Exponential convergence of the hp-version of the composite Gauss-Legendre quadrature for integrals with endpoint singularities
Exponential convergence of the hp-version of the composite Gauss-Legendre quadrature for integrals with endpoint singularities
复制标题
具有端点奇点的积分的复合高斯-勒让德求积的 hp 版本的指数收敛
DOI：
10.1016/j.apnum.2021.08.003
复制
发表时间：
2021
影响因子：
2.8
通讯作者：
Lijun Yi
中科院分区：
文献类型：
--
作者：
Mingzhu Zhang;Xinyu Mao;Lijun Yi
In this paper we propose and analyze anhp-version of the composite Gauss-Legendre quadrature rule which includes local subdivision of the integration domain and local variation of the number of quadrature nodes employed on each subinterval. We derive an a priori error estimate that is fully explicit in the local length of each subinterval, in the local number of quadrature nodes employed on each subinterval, and in the local regularity of the integrand. In particular, for integrands with singularities at one or both endpoints, we prove that exponential convergence can be achieved by using geometric partition of the integration domain and linearly increasing of the number of quadrature nodes in successive subintervals. Numerical experiments are provided to illustrate the theoretical results.
