demo_interpol.m

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function demo_interpol
%function femo_interpol
% Script using femdiscfunc for interpolating functions by local and
% global evaluations.

% B. Haasdonk, I. Maier 26.04.2011

disp('-------------------------------');
disp('     FE-interpolation demo     ');
disp('-------------------------------');

% poisson_model
params = [];
pdeg = 4;
params.pdeg = pdeg;
params.dimrange = 1;
params.numintervals = 5;
% model with evaluations via global coordinates
model = poisson_model(params);
% convert to model allowing local grid evaluations:
model = elliptic_discrete_model(model);
grid = construct_grid(model);
%tmp = load('circle_grid');
%grid = triagrid(tmp.p,tmp.t,[]);
disp('model initialized');

% interpolate exact solution and other coefficient functions 
% as fem-function and plot

disp('examples of interpolation of analytical functions:');
df_info=feminfo(model,grid);
df = femdiscfunc([],df_info);

df = fem_interpol_global(model.solution, df);  
plot(df);
title('analytical solution');

% discretize source function and plot

%df = fem_interpol_local(model.source, df);
df = fem_interpol_global(model.source, df); 
figure,plot(df);
title('source function');

% interpolation of explicit inline function x^2+y^2:
f = @(glob,params) glob(:,1).^2 + glob(:,2).^2;
df = fem_interpol_global(f, df); 
figure,plot(df);
title('function handle for x^2+y^2');

% interpolation of df in finer fem space:
par.pdeg = 4;   
par.qdeg = 8;
par.dimrange = 1;    
p4_df_info = feminfo(par,df.grid);
df2 = femdiscfunc([],p4_df_info);
df_local_eval = @(grid,elids,lcoord,params) ...
      fem_evaluate(df,elids,lcoord,[],[]);
%         my_local_eval(grid,elids,lcoord,params,df); 
df2 = fem_interpol_local(df_local_eval,df2);
figure,plot(df2);
title('local interpolation of discrete function');