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Pré-Publication, Document De Travail Année : 2023

Arbitrary order monotonic finite-volume schemes for 2D elliptic problems

Résumé

Monotonicity is very important in most applications solving elliptic problems. Many schemes preserving positivity has been proposed but are at most second-order convergent. Besides, in general, high-order schemes do not preserve positivity. In the present paper, we propose an arbitrary-order monotonic method for elliptic problems in 2D. We show how to adapt our method to the case of a discontinuous and/or tensorvalued diffusion coefficient, while keeping the order of convergence. We assess the new scheme on several test problems.
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Dates et versions

cea-04211874 , version 1 (20-09-2023)

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  • HAL Id : cea-04211874 , version 1

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Xavier Blanc, Francois Hermeline, Emmanuel Labourasse, Julie Patela. Arbitrary order monotonic finite-volume schemes for 2D elliptic problems. 2023. ⟨cea-04211874⟩
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