Abstract

Fourth-order hyperbolic equations model complex vibration and wave phenomena, and have broad applications in physics and engineering. This paper investigates a split mixed finite element method for such equations. By introducing intermediate variables, the fourth-order differential equation is reformulated as a system of lower-order equations. A semi-discrete split scheme is constructed, and the existence and uniqueness of its solution are established. Error estimates are derived using elliptic projection and the $L^2$-projection operator. A fully discrete split mixed finite element scheme is developed by applying the central difference method to discretize the time derivatives. The stability and convergence of the scheme are analyzed. Numerical experiments for a one-dimensional fourth-order hyperbolic equation validate the theoretical results.

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