Lumped mass matrix in explicit finite element method for transient dynamics of elasticity

The mass matrix of structural dynamics is discussed for the approximations by linear elements with constant Jacobians. The a-priori error estimate is derived for the explicit finite element method using diagonal mass matrix. With smooth solutions, it is shown that by using diagonal mass matrix or consistent mass matrix, the displacement, velocity, and the energies have the same convergence rates. In fact, the difference in numerical errors by these two methods is of order h2. The same conclusion is valid for a certain type of Reissner–Mindlin plate element for transient dynamics.