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arXiv · 1411.7572

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

Emmanuil H. Georgoulis·Omar Lakkis·Charalambos Makridakis·Juha M. Virtanen
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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.

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Emmanuil H. Georgoulis, Omar Lakkis, Charalambos Makridakis, Juha M. Virtanen. 2014-11-27. A posteriori error estimates for leap-frog and cosine methods for second order evolution problems. https://doi.org/10.1137/140996318

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