Seminar in Numerical Analysis: Gilles Vilmart (Université de Genève)

Superconvergence of the Strang splitting when using the Crank-Nicolson scheme for parabolic PDEs with oblique boundary conditions

We show that the Strang splitting method applied to a diffusion-reaction equation with inhomogeneous general oblique boundary conditions is of order two when the diffusion equation is solved with the Crank-Nicolson method, while order reduction occurs in general if using other Runge-Kutta schemes or even the exact flow itself for the diffusion part. We also show that this method recovers stationary states in contrast with splitting methods in general.We prove these results when the source term only depends on the space variable. Numerical experiments suggest that the second order of convergence persists with general nonlinearities.

This is joint work with Guillaume Bertoli (Université de Genève) and Christophe Besse (Institut de Mathématiques de Toulouse).

For further information about the seminar, please visit this webpage.

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