On the smoothing property of the crank-nicolson scheme

Abstract

The Crank-Nicolson scheme for discretizing linear parabolic equations converges at the rate of only o(1) in L ² for initial data in L ². It is shown that smoothing by adding four backward Euler steps to the scheme improves the convergence rate to 0(k ²/t ²).

AMS(MOS): 65M10

†Supported by the NSF Grant MCS-810-1631.

Supported by the DFG, SFB 72 Universität Bonn.

†Supported by the NSF Grant MCS-810-1631.

Supported by the DFG, SFB 72 Universität Bonn.

Notes

†Supported by the NSF Grant MCS-810-1631.

Supported by the DFG, SFB 72 Universität Bonn.

Additional information

Notes on contributors

Wolfgang Wendland