  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.
