Anhp-version of theC0-continuous Petrov-Galerkin time stepping method for nonlinear second-order initial value problems

被引：8
|
作者：
Wei, Yichen [1 ]
Yi, Lijun [1 ]
机构：
[1] Shanghai Normal Univ, Dept Math, Shanghai 200234, Peoples R China
来源：
ADVANCES IN COMPUTATIONAL MATHEMATICS | 2020年 / 46卷 / 04期
基金：
中国国家自然科学基金;
关键词：
hp-version; C-0-continuous Petrov-Galerkin method; Time stepping scheme; Second-order initial value problems; Exponential convergence; FINITE-ELEMENT-METHOD; H-P VERSION; PRIORI ERROR ANALYSIS; INTEGRODIFFERENTIAL EQUATIONS;
D O I：
10.1007/s10444-020-09800-3
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
We present anhp-version of theC(0)-continuous Petrov-Galerkin time stepping method for nonlinear second-order initial value problems. We derive a priori error bound in theH(1)-norm that is fully explicit with respect to the local time steps and the local approximation orders. Moreover, we prove that thehp-version of theC(0)-continuous Petrov-Galerkin time stepping method based on geometrically refined time steps and on linearly increasing approximation orders yields exponential rates of convergence for solutions with start-up singularities. Numerical examples confirm the theoretical results.
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页数：25
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