Two-time level ADI finite volume method for a class of second-order hyperbolic problems

In this paper, we develop a two-time level alternating direction implicit (ADI) method for a class of second-order hyperbolic problems on a rectangular domain. The method builds on the finite volume method with biquadratic basis functions for the discretization in space, and a Crank–Nicolson approach for the time stepping. We obtain a second-order error estimation in the H1H1 norm. Numerical experiments are performed to demonstrate the theoretical findings.