A variational basis for error analysis in finite element elastodynamic problems

Furthermore, it has been observed that variationally correct and conforming formulations satisfy the projection theorems that result from the weak forms of elastodynamic problems by virtue of the virtual work principle. These formulations involve consistent mass matrices and yield eigenfrequencies that are always higher than the analytical values, independent of domain discretisation. This is not necessarily true for variationally incorrect lumped mass formulations in which no guarantee of the boundedness of the eigenvalues with respect to the exact ones can be given. With the help of sweep tests, it has been demonstrated that the computed eigenvalues with lumped mass formulations can be higher than, equal to, or lower than the exact values, depending on the finite element mesh.