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arXiv · 2501.18428

Convergence of a semi-explicit scheme for a one dimensional periodic nonlocal eikonal equation modeling dislocation dynamics

Diana Al Zareef·Ahmad El Hajj·Hassan Ibrahim·Antoine Zurek
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Abstract

In this paper, we derive a periodic model from a one dimensional nonlocal eikonal equation set on the full space modeling dislocation dynamics. Thanks to a gradient entropy estimate, we show that this periodic model converges toward the initial one when the period goes to infinity. Moreover, we design a semi-explicit numerical scheme for the periodic model that we introduce. We show the well-posedness of the scheme and a discrete gradient entropy inequality. We also prove the convergence of the scheme and we present some numerical experiments.

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Diana Al Zareef, Ahmad El Hajj, Hassan Ibrahim, Antoine Zurek. 2025-01-30. Convergence of a semi-explicit scheme for a one dimensional periodic nonlocal eikonal equation modeling dislocation dynamics. https://arxiv.org/abs/2501.18428

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