The next seminar “Modelling of materials – theory, model reduction and efficient numerical methods” will take place on Wednesday from 9:00 till 10:00 in the room K3. The talk will be given by Bangwei She. Please see the details below.
Speaker: Bangwei She
Title: A linear and monolithic FEM for fluid-shell interaction: stability and error estimates
Abstract: We propose a linear and monolithic scheme for the approximation of a fluid-structure interaction problem, that is a flexible elastic plate interacting with a viscous incompressible fluid. For the time discretization we take the backward Euler method. Concerning the space discretization, we use P1-bubble/P1/P1 elements for the approximation of the fluid velocity, pressure, and the structure displacement. With the application of the arbitrary-Lagrange-Euler (ALE) method we derived a linear scheme on the reference domain, meaning that re-meshing is not needed during the simulation. We prove the unconditional stability of the numerical solution as well as the linear convergence rate with respect to the size of the time step ?t and mesh h. Finally, we present the numerical experiments to validate the theoretical results.