-- FreeFem++ v  3.320001 (date Ven  7 nov 2014 14:28:55 CET)
 Load: lg_fem lg_mesh lg_mesh3 eigenvalue 
    1 : //  Discussion:
    2 : //
    3 : //    -del p del(u) = 0  in [-1,+1]x[-1,+1].
    4 : //                u = g  on the boundary.
    5 : //
    6 : //    p = a1*I in Q1 and Q3
    7 : //      = a2*I in Q2 and Q4
    8 : //    f = 0
    9 : //    g = r^gamma * mu(theta)
   10 : //
   11 : //    mu(theta) = 
   12 : //    Q1: cos ( gamma * ( pi/2-sigma) ) * cos ( gamma * ( theta-pi/2+rho )    )
   13 : //    Q2: cos ( gamma *          rho  ) * cos ( gamma * ( theta-pi+sigma )    )
   14 : //    Q3: cos ( gamma *        sigma  ) * cos ( gamma * ( theta-pi-rho )      )
   15 : //    Q4: cos ( gamma * ( pi/2 - rho) ) * cos ( gamma * ( theta-3pi/2-sigma ) )
   16 : //
   17 : //    Parameter values:
   18 : //
   19 : //      a1 = 161.4476387975881
   20 : //      a2 = 1.0
   21 : //      gamma = 0.1
   22 : //      rho = pi / 4
   23 : //      sigma = -14.92256510455152
   24 : //
   25 : //    Note that the formulation in the Mitchell reference uses different
   26 : //    names for variables, a somewhat different formulation for mu(theta),
   27 : //    some typographical errors, and does not seem to produce the result
   28 : //    displayed in the figure.  The data and formulation from the Morin
   29 : //    reference seems more satisfactory.
   30 : //
   31 : //    I CANNOT get this problem to give me anything like the results 
   32 : //    displayed by Mitchell, nor can I explain the lack of symmetry.
   33 : //
   34 : //  Location:
   35 : //
   36 : //    http://people.sc.fsu.edu/~jburkardt/examples/mitchell_freefem++/test11.edp
   37 : //
   38 : //  Licensing:
   39 : //
   40 : //    This code is distributed under the GNU LGPL license.
   41 : //
   42 : //  Modified:
   43 : //
   44 : //    09 February 2015
   45 : //
   46 : //  Author:
   47 : //
   48 : //    John Burkardt
   49 : //
   50 : //  Reference:
   51 : //
   52 : //    Frederic Hecht,
   53 : //    Freefem++,
   54 : //    Third Edition, version 3.22
   55 : //
   56 : //    William Mitchell,
   57 : //    A collection of 2D elliptic problems for testing adaptive
   58 : //    grid refinement algorithms,
   59 : //    Applied Mathematics and Computation,
   60 : //    Volume 220, 1 September 2013, pages 350-364.
   61 : //
   62 : //    Pedro Morin, Ricardo Nochetto, Kunibert Siebert,
   63 : //    Data oscillation and convergence of adaptive FEM,
   64 : //    SIAM Journal on Numerical Analysis,
   65 : //    Volume 38, Number 2, 2000, pages 466-488.
   66 : //
   67 : 
   68 : //
   69 : //  Set parameters.
   70 : //
   71 : real a1 = 161.4476387975881;
   72 : real a2 = 1.0;
   73 : real gam = 0.1;
   74 : real rho = pi / 4.0;
   75 : real sigma = -14.92256510455152;
   76 : //
   77 : //  Set the borders.
   78 : //
   79 : border bottom ( t = -1.0,  1.0 )  { x = t;     y = -1.0; label = 1; }
   80 : border right  ( t = -1.0,  1.0 )  { x = 1.0;   y = t;    label = 1; }
   81 : border top    ( t =  1.0, -1.0 )  { x = t;     y = +1.0; label = 1; }
   82 : border left   ( t =  1.0, -1.0 )  { x = -1.0;  y = t;    label = 1; }
   83 : //
   84 : //  Define Th, the triangulation of the "left" side of the boundaries.
   85 : //
   86 : int n = 20;
   87 : mesh Th = buildmesh ( bottom ( n ) + right ( n ) + top ( n ) + left ( n ) );
   88 : //
   89 : //  Define Vh, the finite element space defined over Th, using P1 basis functions.
   90 : //
   91 : fespace Vh ( Th, P1 );
   92 : //
   93 : //  Define U, V, and F, piecewise continuous functions over Th.
   94 : //
   95 : Vh u;
   96 : Vh v;
   97 : //
   98 : //  Define the exact solution function G = r^gam * mu(theta).
   99 : //
  100 : //func g {
  101 : //func real g ( real xx, real yy )
  102 : func g
  103 : {
 Error line number 103, in file test11.edp, before  token {
syntax error
  current line = 102
Compile error : syntax error
	line number :103, {
error Compile error : syntax error
	line number :103, {
 code = 1 mpirank: 0