Speaker
Nils Bullerjahn
Description
In this talk we analyse a bulk--surface finite element in space and backward difference in time full discretization of a general two-parameter family of Cahn--Hilliard equations with dynamic boundary conditions. A novel proof strategy using discrete almost mass conservation and a suitable Poincaré–Wirtinger inequality is presented to achieve optimal-order fully discrete error estimates in the $L^2$- and $H^1$-norm. Additionally, we present an adaptive algorithm in time and space with estimators originating from a residual based a posteriori error analysis. Numerical examples illustrate and validate the theoretical results.