So, DMDA is used for sparse matrices arising from FD/FE and MatCreateMPIAIJ can be used for dense matrices (though it is strongly discouraged).
My confusion stemmed from DMDAGetElements giving the element indices for the 1D mesh/vector of size N(when the DMDACreate1d is used). But these indices were then used as local indices to set the values for a 2D matrix (via MatSetValuesLocal ) created using the same DM (now we have NxN elements).
