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

Numerical results validate this observation.