Error(ue,xp,uh)

function [L2err,H1err,LI0err] = Error(ue,xp,uh)
% function that calculates three different errors
% the discrete L2error, the discrete H1error and the L_inf error
%
% input:   o ue.......the exact solution as function_handle
%          o xp.......vector containing the gridpoints
%          o uh.......vector containing the numerical solution
%
% output:  o L2err....error calculated in discrete L2 norm
%          o H1err....error calculated in discrete H1 norm
%          o LI0err...error calculated in L_inf norm
%
% notes:   o for big step sizes the approximated derivation could not fit
%            to the exact one and the H1err could get to big
%          o might be buggy, please mail if you have an improvement...
%
% authors: o Christian Jkel (University of Technology Dresden)
%          o Daniel Klawitter (University of Technology Dresden)


% for H1err we need the derivation of the exact solution
uprime = str2func(['@(x)',char(diff(sym(ue)))]);

% set the errors to zero, for summation
L2err = 0;
H1err = 0;


h = diff(xp);
duh = diff(uh)./h;
for j = 1:length(uh)
    %         L2err = L2err + sqrt(h(j))*(ue(xp(j))-uh(j))^2;
    L2err = L2err + (ue(xp(j))-uh(j))^2;
end
for j = 1:length(duh)
    %L2err = L2err + (ue(xp(j))-uh(j))^2;
    H1err = H1err + ((uprime(xp(j)))-duh(j))^2;
end

H1err = sqrt(mean(h))*sqrt(H1err + L2err);
L2err = sqrt(mean(h))*sqrt(L2err);

    



for k = 1:length(xp)
    uex(k) = ue(xp(k));
end

LI0err = max(abs(uex-uh));