2024/05/30 by Benoit, Antoine, Coulombel, Jean-François
#FOS: Mathematics #Numerical Analysis (math.NA)
paper · doi:10.48550/arxiv.2405.19844
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.