Complexity bounds on supermesh construction for quasi-uniform meshes

Projecting fields between different meshes commonly arises in computational physics. This operation may 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 and cells respectively, we show under standard assumptions that n is proportional to . This result substantially improves on the best currently available upper bound on n and is fundamental for the analysis of algorithms that use supermeshes.