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arXiv · 2405.19844

The Neumann boundary condition for the two-dimensional Lax-Wendroff scheme. II

Antoine Benoit·Jean-François Coulombel
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Abstract

We study the stability of a two-dimensional Lax-Wendroff scheme in a quarter-plane. Following our previous work, we aim here at adapting the energy method in order to study second order extrapolation boundary conditions. We first show on the one-dimensional problem why modifying the energy is a necessity in order to obtain stability estimates. We then study the two-dimensional case and propose a modified energy as well as second order extrapolation boundary and corner conditions in order to maintain second order accuracy and stability of the whole scheme, including near the corner.

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Antoine Benoit, Jean-François Coulombel. 2024-05-30. The Neumann boundary condition for the two-dimensional Lax-Wendroff scheme. II. https://arxiv.org/abs/2405.19844

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