Complexity bounds on supermesh construction for quasi-uniform meshes

Projecting fields between different meshes commonly arises in computational
physics. This operationmay require a supermesh
construction and in this case its computational cost is proportional to the number of cells of the supermesh $n$. Given any two
quasi-uniform meshes of $n_A$ and $n_B$ cells respectively, we show under
standard assumptions that n is proportional to $n_A + n_B$. This result
substantially improves on the best currently available upper bound on $n$ and
is fundamental for the analysis of algorithms that use supermeshes.