function L = plate_laplacian(wp, dx, dy)
% PLATE_LAPLACIAN  Five-point Laplacian of a padded field.
%
%   L = plate_laplacian(wp, dx, dy) takes an (ny+2) x (nx+2) array with one
%   ghost layer (see plate_pad) and returns the ny x nx second-order
%   approximation of w_xx + w_yy at every node of the original grid.
%   Rows index y and columns index x.

L = (wp(3:end, 2:end - 1) - 2 * wp(2:end - 1, 2:end - 1) + wp(1:end - 2, 2:end - 1)) / dy^2 ...
  + (wp(2:end - 1, 3:end) - 2 * wp(2:end - 1, 2:end - 1) + wp(2:end - 1, 1:end - 2)) / dx^2;
end