We present a novel dynamic approach for solid-fluid coupling by joining two different numerical methods: the boundary-element method (BEM) and the finite element method (FEM). The FEM results describe the thermomechanical evolution of the solid while the fluid is solved with the BEM. The bidirectional feedback between the two domains evolves along a Lagrangian interface where the FEM domain is embedded inside the BEM domain. The feedback between the two codes is based on the calculation of a specific drag tensor for each boundary on finite element. The approach is presented here to solve the complex problem of the descent of a cold subducting oceanic plate into a hot fluid-like mantle. The coupling technique is shown to maintain the proper energy dissipation caused by the important secondary induced mantle flow induced by the lateral migrating of the subducting plate. We show how the method can be successfully applied for modelling the feedback between deformation of the oceanic plate and the induced mantle flow. We find that the mantle flow drag is singular at the edge of the retreating plate causing a distinct hook shape. In nature, such hooks can be observed at the northern end of the Tonga trench and at the southern perimeter, of the South American trench.