function value = elliptic_wavefront_exact ( x, y )

%*****************************************************************************80
%
%% ELLIPTIC_WAVEFRONT_EXACT evaluates the exact solution.
%
%  Modified:
%
%    05 November 2013
%
%  Author:
%
%    John Burkardt
%
%  Reference:
%
%    William Mitchell,
%    A collection of 2D elliptic problems for testing adaptive
%    grid refinement algorithms,
%    Applied Mathematics and Computation,
%    Volume 220, 1 September 2013, pages 350-364.
%
%  Parameters:
%
%    Input, real X(*), Y(*), evaluation points.
%
%    Output, real VALUE(*), the exact solution at the evaluation points.
%
  alpha = 20.0;
  xc = - 0.05;
  yc = - 0.05;
  r0 = 0.7;

  r = sqrt ( ( x - xc ).^2 + ( y - yc ).^ 2 );
  value = atan ( alpha * ( r - r0 ) );

  return
end
