An L∞L∞ stability analysis for the finite-difference solution of one-dimensional linear convection–diffusion equations on moving meshes

The stability of three moving-mesh finite-difference schemes is studied in the L∞L∞ norm for one-dimensional linear convection–diffusion equations. These schemes use central finite differences for spatial discretization and the θθ method for temporal discretization, and they are based on conservative and non-conservative forms of transformed partial differential equations. The stability conditions obtained consist of the CFL condition and the mesh speed related conditions. The CFL condition is independent of the mesh speed and has the same form as that for fixed meshes. The mesh speed related conditions restrict how fast the mesh can move. The conditions of this type obtained in this paper are weaker than those in the existing literature and can be satisfied when the mesh is sufficiently fine. Illustrative numerical results are presented.