A numerical approach for fluid deformable surfaces with conserved enclosed volume

We consider surface finite elements and a semi-implicit time stepping scheme to simulate fluid deformable surfaces. Such surfaces are modeled by incompressible Navier-Stokes equations with bending forces. Here, we closed enforce conservation of the enclosed volume. The numerical approach builds on higher order parameterizations, Taylor-Hood element for part, appropriate approximations geometric quantities surface, mesh redistribution Lagrange multiplier constraint. considered computational examples highlight solid-fluid duality demonstrate convergence properties that known be optimal different sub-problems.