Non Uniform Meshing in 1D Fem

Hello, I am developing a 1D fem problem, I know how to create a uniform mesh, but does any one know how to create a non uniform mesh AFTER the uniform mesh is created.

For eg, if we have 5 elements, we have 6 nodes created, but now the user wants to create another node between 4 and 5 node. This would result in 6 elements and 7 nodes.

Does anyone know how to do that? or any links, here is my code, so far

%number of elements the solution 1D FEM

nE=3;

xb = 1

xa = 0

%generate nodes

nN=nE+1;

if nE<1

error('Number of elements <1');

end

%initiliasation ( speeds up calculations)

Nod= zeros(nN,1);

Elm = zeros(nE,2);

%generate list of nodes

for i=1:1:nN

Nod(i,1) = xa + (i-1)*(xb-xa)/nE;

end

%generate connectivity array for elelments

for k=1:1:nE

Elm(k,1)=k;

Elm(k,2)=k+1;

end