Symplectic-mixed finite element approximation of linear acoustic wave equations

We apply mixed finite element approximations to the first-order form of the acoustic wave equation. The semidiscrete method exactly conserves the system energy. A fully discrete method employing the symplectic Euler time method in time exactly conserves a positive-definite pertubed energy functional that is equivalent to the actual energy under a CFL condition. In addition to proving optimal-order L∞(L2) estimates, we also develop a bootstrap technique that allows us to derive stability and error bounds for the time derivatives and divergence of the vector variable beyond the standard under some additional regularity assumptions.