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.

引用

页数：25

共 29 条

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