Volume 63, pp. 320-356, 2025.

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

Antoine Benoit and Jean-François Coulombel

Abstract

We study the stability of a two-dimensional Lax-Wendroff scheme in a quarter-plane. Following our previous work in [Commun. Math. Sci., 21 (2023), pp. 2051–2082], we aim here at adapting the energy method in order to study second-order extrapolation boundary conditions. We first show, based 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.

Full Text (PDF) [413 KB], BibTeX , DOI: 10.1553/etna_vol63s320

Key words

transport equations, numerical schemes, domains with corners, boundary conditions, stability

AMS subject classifications

65M12, 65M06, 65M20