A Crank-Nicolson Leapfrog stabilization: Unconditional stability and two applications

We propose and analyze a linear stabilization of the Crank-Nicolson Leapfrog (CNLF) method that removes all time step/CFL conditions for stability and controls the unstable mode. It also increases the SPD part of the linear system to be solved at each time step while increasing solution accuracy. We give a proof of unconditional stability of the method as well as a proof of unconditional, asymptotic stability of both the stable and unstable modes. We illustrate two applications of the method: uncoupling groundwater-surface water flows and Stokes flow plus a Coriolis term.