Continuous Galerkin methods on quasi-geometric meshes for delay differential equations of pantograph type
Continuous Galerkin methods on quasi-geometric meshes for delay differential equations of pantograph type
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DOI：
10.3934/dcds.2016039
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发表时间：
2016-07
影响因子：
1.1
通讯作者：
Qiumei Huang;Xiuxiu Xu;H. Brunner
中科院分区：
文献类型：
--
作者：
Qiumei Huang;Xiuxiu Xu;H. Brunner
研究了一类比例时滞微分方程的连续Galerkin（CG）解在拟几何网格上的最优全局收敛性和局部收敛性。结果表明，在这类网格下，CG解的节点超收敛阶数比均匀网格下的高。理论结果说明了广泛的数值例子。
We analyze the optimal global and local convergence properties of continuous Galerkin (CG) solutions on quasi-geometric meshes for delay differential equations with proportional delay. It is shown that with this type of meshes the attainable order of nodal superconvergence of CG solutions is higher than of the one for uniform meshes. The theoretical results are illustrated by a broad range of numerical examples.