Second-order bulk-surface splitting for the wave equation with kinetic boundary conditions

Abstract

This paper is devoted to the numerical analysis of a second-order bulk--surface splitting scheme for the semi-linear wave equation with kinetic boundary conditions. The construction is based on the interpretation of the equations as coupled system and the implementation of different difference formulae for the discrete states depending on their exact position in the system equations. This results in a 4-step scheme which decouples bulk and surface dynamics. We prove energy stability and second-order convergence under a weak CFL condition and validate these results also numerically.