  This paper introduces a mathematical framework for explicit structural
dynamics, employing approximate dual functionals and rowsum mass lumping. We
demonstrate that the approach may be interpreted as a Petrov-Galerkin method
that utilizes rowsum mass lumping or as a Galerkin method with a customized
higher-order accurate mass matrix. Unlike prior work, our method correctly
incorporates Dirichlet boundary conditions while preserving higher order
accuracy. The mathematical analysis is substantiated by spectral analysis and a
two-dimensional linear benchmark that involves a non-linear geometric mapping.
Our results reveal that our approach achieves accuracy and robustness
comparable to a traditional Galerkin method employing the consistent mass
formulation, while retaining the explicit nature of the lumped mass
formulation.
