\(H^1\)-Galerkin mixed finite element methods for pseudo-hyperbolic equations (Q1026321)

The authors propose \(H^{1}\)-Galerkin mixed finite element schemes for a class of second-order pseudo-hyperbolic equations. Depending on the physical quantities of interests, two methods are discussed. Optimal error estimates are obtained for both semidiscrete and completely discrete schemes in a single space variable. An extension to problems in two and three space variables is also discussed, existence and uniqueness are derived and it is shown that the \(H^{1}\)-Galerkin mixed finite element approximations have the same rate of convergence as in the classical mixed finite element methods without requiring the Ladyshenskaya-Babuška-Brezzi (LBB) consistency condition. It shall be pointed out that the considered second-order pseudo-hyperbolic equations are a type of dual-phase-lagging heat transport equations.