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A posteriori error estimates for leap-frog and cosine methods for second order evolution problems

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posted on 2017-08-17, 10:27 authored by Emmanuil H. Georgoulis, Omar Lakkis, Charalambos G. Makridakis, Juha M. Virtanen
We consider second order explicit and implicit two-step time-discrete schemes for wave-type equations. We derive optimal order a posteriori estimates controlling the time discretization error. Our analysis has been motivated by the need to provide a posteriori estimates for the popular leap-frog method (also known as Verlet's method in the molecular dynamics literature); it is extended, however, to general cosine-type second order methods. The estimators are based on a novel reconstruction of the time-dependent component of the approximation. Numerical experiments confirm similarity of the convergence rates of the proposed estimators and the theoretical convergence rate of the true error.

History

Citation

SIAM Journal on Numerical Analysis, 2016, 54 (1), pp. 120-136

Author affiliation

/Organisation/COLLEGE OF SCIENCE AND ENGINEERING/Department of Mathematics

Version

  • VoR (Version of Record)

Published in

SIAM Journal on Numerical Analysis

Publisher

Society for Industrial and Applied Mathematics

issn

0036-1429

eissn

1095-7170

Acceptance date

2015-10-12

Copyright date

2016

Available date

2017-08-17

Publisher version

http://epubs.siam.org/doi/10.1137/140996318

Notes

AMS Subject Headings 35L05, 37M05, 37M15, 65M60, 65N50

Language

en

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