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

We propose and analyze a linear stabilization of the Crank-Nicolson Leap-Frog (CNLF) method that removes all timestep / 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. 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.