$L^2$ norm error estimates of semi- and full discretisations, using bulk--surface finite elements and Runge--Kutta methods, of wave equations with dynamic boundary conditions are studied. The analysis resides on an abstract formulation and error estimates, via energy techniques, within this abstract setting. Four prototypical linear wave equations with dynamic boundary conditions are analysed which fit into the abstract framework. For problems with velocity terms, or with acoustic boundary conditions we prove surprising results: for such problems the spatial convergence order is shown to be less than two. These can also be observed in the presented numerical experiments.

Dr. Balázs Kovács works on developing new computational algorithms, with rigorous numerical analysis, for partial differential equations in bounded domains with dynamic boundary conditions and partial differential equations on evolving surfaces. He is currently a postdoc at Eberhard Karls Universität Tübingen (Germany), and he earned his PhD in mathematics from Eötvös Loránd University (Hungary) in 2015.