How to avoid mass matrix for linear hyperbolic problems

We are interested in the numerical solution of linear hyperbolic problems using continuous finite elements of arbitrary order. It is well known that this kind of methods, once the weak formulation has been written, leads to a system of ordinary differential equations in $\R^N$, where $N$ is the number of degrees of freedom. The solution of the resulting ODE system involves the inversion of a sparse mass matrix that is not block diagonal. Here we show how to avoid this step, and what are the consequences of the choice of the finite element space. Numerical examples show the correctness of our approach.