An Eulerian time‐stepping scheme for a coupled parabolic moving domain problem using equal‐order unfitted finite elements

We consider an unfitted Eulerian time-stepping scheme for a coupled parabolic model problem on moving domain. In this model, the domain motion results from ordinary differential equation to bulk via forces acting interface. extend our initial work (von Wahl & Richter, 2022) allow equal-order finite element discretisations partial and Lagrange multiplier spaces. Together with BFD2 scheme, lowest-order case of method then in fully balanced second-order space time. show that has same stability properties as work. Numerical validate observation.