An hp-version of the C0-continuous Petrov-Galerkin method for second-order Volterra integro-differential equations

被引：3
|
作者：
Li, Shuangshuang [1 ]
Wang, Lina [1 ]
Yi, Lijun [1 ]
机构：
[1] Shanghai Normal Univ, Dept Math, Shanghai 200234, Peoples R China
来源：
APPLIED NUMERICAL MATHEMATICS | 2020年 / 152卷
基金：
中国国家自然科学基金;
关键词：
Second-order Volterra integro-differential equations; hp-version; Continuous Petrov-Galerkin method; FINITE-ELEMENT-METHOD; POLYNOMIAL SPLINE COLLOCATION; WEAKLY SINGULAR KERNEL; SPECTRAL-COLLOCATION; INTEGRAL-EQUATIONS; P VERSION; SMOOTH; TIME; CONVERGENCE; DISCRETIZATION;
D O I：
10.1016/j.apnum.2020.01.017
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
We present an hp-version of the C-0-continuous Petrov-Galerkin method for linear second-order Volterra integro-differential equations. We combine the continuous and discontinuous Galerkin methodologies to obtain a natural discretization of the second order derivative of arbitrary order. We derive a-priori error bounds in the L-2- and H-1-norm that are completely explicit in the local time steps, local approximation orders, and local regularity of the exact solution. Numerical experiments are provided to illustrate the theoretical results. (C) 2020 IMACS. Published by Elsevier B.V. All rights reserved.
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页码：84 / 104
页数：21
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