discfunc/ldg/ldg_l2project.m

function dofs = ldg_l2project(func,qdeg,df_info)
%function dofs = ldg_l2project(func,qdeg,df_info)
%
% function performing an l2 projection of an analytic function func to
% the ldg space. A quadrature of degree qdeg is used.
% 'params.dimrange' and 'params.pdeg' specify the discrete function space.
%
% func is a function to be called with local coordinates 
% 'res = func(einds, locs ,grid,params)'
% 'res' is a matrix of 'size(locs,2) x dimrange'
%
% using the notation as explained in ldgdiscfunc.m, the projection computes
% df such that <df - func, `\phi_j`> = 0 for all global basis
% functions `\phi_j`
%
% This yields (using simple domain transformations, determinant
% cancles out by division)
%
% ``\mbox{dof}(j) = \frac{<\mbox{func}, \phi_j>}{|det(F_T(j)x)|} =
%                   \int_{\hat T} \mbox{func}(F(\hat x)) \hat \phi_i(j) (\hat x)``

% Bernard Haasdonk 2.2.2009

% simply pass func_phi_product and its parameters to quadrature routine.

% fast implementation:
%params.evaluate_basis = @ldg_evaluate_basis;
dofs = triaquadrature(qdeg,@func_phi_product,func,df_info);
%dofs = dofs(:);

% generic implementation:
%params.element_quadrature = @triaquadrature;
%params.local_mass_matrix = @ldg_local_mass_matrix;
%dofs = l2project(func,qdeg,grid,params);

%| \docupdate