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

https://doi.org/10.1016/j.cam.2014.09.026Get rights and content
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Abstract

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.

MSC

65L20
65M12

Keywords

CNLF
Stabilization
CFL condition

Cited by (0)

This report is in final form. The research of the authors was partially supported by National Science Foundation grant DMS 1216465 and Air Force Office of Scientific Research grant FA 9550-12-1-0191.