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

Georgoulis, Emmanuil H, Lakkis, Omar, Makridakis, Charalambos G and Virtanen, Juha M (2016) A posteriori error estimates for leap-frog and cosine methods for second order evolution problems. SIAM Journal on Numerical Analysis (SINUM), 54 (1). pp. 120-136. ISSN 0036-1429

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Abstract

We consider second order explicit and implicit two-step time-discrete schemes for wave-type equations. We derive optimal order aposteriori estimates controlling the time discretization error. Our analysis, has been motivated by the need to provide aposteriori estimates for the popular leap-frog method (also known as Verlet's method in 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 convergence rates of the proposed estimators and of the theoretical convergence rate of the true error.

Item Type: Article
Additional Information: arXiv: 1411.7572
Keywords: Mathematics, Numerical Analysis, finite element, Verlet, leapfrog, wave equation, hyperbolic, time stepping, explicit scheme, staggered grids
Schools and Departments: School of Mathematical and Physical Sciences > Mathematics
Subjects: Q Science > QA Mathematics > QA0297 Numerical analysis
Q Science > QA Mathematics > QA0299 Analysis. Including analytical methods connected with physical problems
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Depositing User: Omar Lakkis
Date Deposited: 16 Feb 2016 08:47
Last Modified: 23 Aug 2017 18:54
URI: http://sro.sussex.ac.uk/id/eprint/59658

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