eop_space_time_norm.m

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function norm = eop_space_time_norm(fd_function1, fd_function2, grid, ~)
%norm = eop_space_time_norm(fd_function1, fd_function2, grid, ~)
%
% function which computes the space-time norm ||u|| = sqrt(sum_k <u^k,u^k>)
% with u^k a timeslice, i.e. a column of a respective function, and <.,.>
% being the discrete L2-SP. With two inputfuntions you compute the error
% ||fd_function1 - fd_function2|| and with one of them being zero you
% compute the norm of the other.
%
% fd_function1 and fd_function2 have to have the same size and they are
% assumed to be in matrix-form, i.e. one column represents the function in
% one timeslice.
%
% grid is for example model_data.grid

% Dominik Garmatter 27.07 2012

A = speye(grid.nvertices)*1/grid.nvertices; % mass matrix of the discrete L2-SP
C = fd_function1-fd_function2;
norm_build = 0;

for i = 1:size(C,2)
    skalarproduct = C(:,i)'*A*C(:,i);
    norm_build = norm_build + skalarproduct;
end
norm = sqrt(norm_build);