Variational Mass Lumping in the Partition of Unity Method

This paper is concerned with the construction of a variational mass lumping scheme for the partition of unity methods. The presented approach is applicable to arbitrary local approximation spaces and any nonnegative partition of unity. We give improved error bounds for the partition of unity method using a nonnegative partition of unity and show that our lumped mass matrix is conservative at least for any $f \in V{\rm PU}$ such that $f