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arXiv · 2404.15947

Adapted Lie splitting method for convection-diffusion problems with singular convective term

Thi Tam Dang·Trung Hau Hoang·Giandomenico Orlandi
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Abstract

Splitting methods are a widely used numerical scheme for solving convection-diffusion problems. However, they may lose stability in some situations, particularly when applied to convection-diffusion problems in the presence of an unbounded convective term. In this paper, we propose a new splitting method, called the "Adapted Lie splitting method", which successfully overcomes the observed instability in certain cases. Assuming that the unbounded coefficient belongs to a suitable Lorentz space, we show that the adapted Lie splitting converges to first-order under the analytic semigroup framework. Furthermore, we provide numerical experiments to illustrate our newly proposed splitting approach.

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Thi Tam Dang, Trung Hau Hoang, Giandomenico Orlandi. 2024-04-24. Adapted Lie splitting method for convection-diffusion problems with singular convective term. https://arxiv.org/abs/2404.15947

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