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| Title
| - Quadratic stability of flux limiters
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| Abstract
| - We propose a novel approach to study the quadratic stability of 2D flux limiters for non expansive transport equations. The theory is developed for the constant coefficient case on a cartesian grid. The convergence of the fully discrete nonlinear scheme is established in 2D with a rate not less than O(Δ x½) in quadratic norm. It is a way to bypass the Goodman-Leveque obstruction Theorem. A new nonlinear scheme with corner correction is proposed. The scheme is formally second-order accurate away from characteristics points, satisfies the maximum principle and is proved to be convergent in quadratic norm. It is tested on simple numerical problems.
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| - © The authors. Published by EDP Sciences, SMAI 2023
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| - The authors. Published by EDP Sciences, SMAI
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