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Title: A posteriori error estimates for leap-frog and cosine methods for second order evolution problems
Authors: Georgoulis, Emmanuil H.
Lakkis, Omar
Makridakis, Charalambos G.
Virtanen, Juha M.
First Published: 14-Jan-2016
Publisher: Society for Industrial and Applied Mathematics
Citation: SIAM Journal on Numerical Analysis, 2016, 54 (1), pp. 120-136
Abstract: 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.
DOI Link: 10.1137/140996318
ISSN: 0036-1429
eISSN: 1095-7170
Version: Publisher Version
Status: Peer-reviewed
Type: Journal Article
Rights: Copyright © 2016, Society for Industrial and Applied Mathematics. Deposited with reference to the publisher’s open access archiving policy.
Description: AMS Subject Headings 35L05, 37M05, 37M15, 65M60, 65N50
Appears in Collections:Published Articles, Dept. of Mathematics

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