fv_h1_inner_product_matrix.m

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function W = fv_h1_inner_product_matrix(model,model_data)
%function W = fv_h1_inner_product_matrix(model,model_data)
% function computing the h1 inner product matrix for fv-functions on the grid.
%
% By this function, inner products between functions can be
% computed by their DOF vectors: `<U_1, U_2>_{H^1,h} = U_1' W U_2`
%
% return values:
%   W        : inner product matrix

% Bernard Haasdonk 20.7.2006

grid = model_data.grid;

% currently simple diagonal weighting of element values sufficient
W = sparse(1:grid.nelements,1:grid.nelements,grid.A);
H = grid.nelements;
i=reshape(repmat([1:H],5,1),5*H,1);
j=reshape([1:H;grid.NBI'],5*H,1);
s=100*grid.DC(1,1) * reshape([-ones(1,H);1/4*ones(4,H)],5*H,1);
s(j<1);
j(j<1)=1;
WH = sparse(i,j,s,H,H,5*H);
W = W + WH' * WH;