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2 results

An Adaptive Time Stepping Method for Transient Dynamic Response Analysis
Part of
- Partial differential equations, initial value and time-dependent initial-boundary value problems
Jianguo Huang, Huashan Sheng
Journal:

East Asian Journal on Applied Mathematics / Volume 6 / Issue 2 / May 2016

Published online by Cambridge University Press:

12 May 2016, pp. 152-170

Print publication:

May 2016
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An efficient adaptive time stepping method is proposed for transient dynamic response analysis, which is frequently encountered in civil engineering and elsewhere. The reduced problem following the spatial discretisation can be discretised in the time by a C0-continuous discontinuous Galerkin method, and the adaptive time stepping strategy is based on optimal a posteriori error estimates developed using the energy method. Some numerical experiments demonstrate the effectiveness of our approach.

An L∞-error Estimate for the h-p Version Continuous Petrov-Galerkin Method for Nonlinear Initial Value Problems
Part of
- Numerical analysis: Ordinary differential equations
Lijun Yi
Journal:

East Asian Journal on Applied Mathematics / Volume 5 / Issue 4 / November 2015

Published online by Cambridge University Press:

10 November 2015, pp. 301-311

Print publication:

November 2015
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The h-p version of the continuous Petrov-Galerkin time stepping method is analyzed for nonlinear initial value problems. An L∞-error bound explicit with respect to the local discretization and regularity parameters is derived. Numerical examples are provided to illustrate the theoretical results.

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2 results

An Adaptive Time Stepping Method for Transient Dynamic Response Analysis

An L∞-error Estimate for the h-p Version Continuous Petrov-Galerkin Method for Nonlinear Initial Value Problems