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.

翻译：我们研究了四分之一平面上二维Lax-Wendroff格式的稳定性。继先前工作之后，本文旨在调整能量方法以研究二阶外推边界条件。我们首先在一维问题上说明为何必须修正能量才能获得稳定性估计。随后我们研究二维情形，提出了修正的能量以及二阶外推边界与角点条件，以保证整个格式（包括角点附近区域）的二阶精度与稳定性。