Speaker
Sebastian Myrbäck, KTH Royal Institute of Technology
Abstract
In this talk I will present a high-order cut finite element method for modeling the evolution of surfactant concentration in a two-phase fluid, described by coupled convection-diffusion equations in evolving domains. By applying Reynolds’ transport theorem in the weak formulation, our method naturally conserves the global mass over time. The method employs a space-time discretization, but the integrals in time are approximated by quadrature rules to produce schemes resembling time-stepping methods and avoid constructing the full space-time domain. Quadrature rules that result in optimal order of convergence in space and time are used. Furthermore, a more efficient stabilization procedure for cut finite element methods is presented by partitioning the time-dependent domain into macroelements. In this approach, stabilization is applied only where needed, leading to an increased sparsity of the resulting system matrix while maintaining control of the condition number and the error independent of the position of the evolving domain relative to the mesh.