test1.m

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%% QMG test 1
%% This is an approximation to the mesh on the cover of Claes 
%% Johnson's book ``Numerical solutions of partial differential
%% equations by the finite element method'' , Cambridge U. Press 1987.
%% It has greater refinement near the origin.


global interactive
wedgeangle = pi / 6.0;

%% Make a circular approximation with 4 Bezier curves from pi/6 to 2pi.

[verts,codes] = gm_circ_approx(wedgeangle, 2*pi, 4);
newverts = [0,0;verts];
newcodes = [0;codes];
domain = gm_cpoly(newverts, newcodes);


% The size function is of the form h0*r^p+f, where p is determined
% by (4.31) in Johnson, and f is determined so that the H1 error on
% the innermost triangles matches the H1 error everywhere else.

h0 =  0.2;
gamma = pi / (2*pi - wedgeangle);
f  = h0 ^ (1.0/gamma);
p = 1.0 - gamma;

sizectl = sprintf('(formula (%d * (%%0^2+%%1^2)^(%d/2.0) + %d))', h0, p, f);

show =  0;
if length(interactive) > 0
  disp(sprintf('size control string = %s', sizectl));
  show = 1;
end

mesh = gmmeshgen(domain, 'size', sizectl, 'show', show);
[scrap, numvtx] = size(mesh{4});
asp  = gmchecktri(domain,mesh);


global aspprod
global meshsizesum
if length(aspprod) > 0
  aspprod = aspprod * asp;
  meshsizesum = meshsizesum + numvtx;
end

if length(interactive) > 0
  gmviz(mesh)
end

% ------------------------------------------------------------------
% Copyright (c) 1999 by Cornell University.  All rights reserved
% See the accompanying file 'Copyright' for authorship information,
% the terms of the license governing this software, and disclaimers
% concerning this software.
% ------------------------------------------------------------------
% This file is part of the QMG software.  
% Version 2.0 of QMG, release date September 3, 1999.
% ------------------------------------------------------------------