We extend the convergence results in Svärd and Nordström (2019) [7] for single-domain energy-stable high-order finite difference schemes, to include domains split into several grid blocks. The analysis also demonstrates that reflective boundary conditions enjoy same properties. Finally, we briefly indicate these (and previous ones [7]) hold multiple dimensions.

Abstract We propose a new finite difference scheme for the degenerate parabolic equation $$\begin{aligned} \partial _t u - \text{ div }(|\nabla u|^{p-2}\nabla u) =f, \quad p\ge 2. \end{aligned}$$ ? t u - ...