H1H1-Galerkin mixed finite element methods for pseudo-hyperbolic equations

H1H1-Galerkin mixed finite element methods are discussed for a class of second-order pseudo-hyperbolic equations. Depending on the physical quantities of interest, two methods are discussed. Optimal error estimates are derived for both semidiscrete and fully discrete schemes for problems in one space dimension. An extension to problems in two and three space variables is also discussed, the existence and uniqueness are derived and it is showed that the H1H1-Galerkin mixed finite element approximations have the same rate of convergence as in the classical mixed finite element methods without requiring the LBB consistency condition.