MathLab seminar announcement

[Emanuele Tuillier Illingworth]

MATHLAB SEMINAR ANNOUNCEMENT


Nicola Cavallini

Title: Finite elements methods for the Immersed Boundary Method

Abstract: In this talk I am going to present finite elements methods 
applied to the Immersed Boundary Method. IBM dates back to ’70 and has 
been firstly introduced by C. S. Peskin in a finite difference 
framework. The finite elements formulation of IBM has to be addressed to 
D. Boffi and L. Gastaldi in the early 2000. L. Heltai, developed this 
technique in his Ph.D. thesis in 2006, supervised by D.B. and L.G.  
Since 2009 IBM dedicated finite elements techniques has been developed 
in Pavia. In a first stage D. B., N. Cavallini, F. Gardini, and L. G, 
worked on enhancing finite elements for the Stokes problem. It is well 
known that one of the drawbacks of IBM methods is diffusivity. In this 
studies we showed how adding discontinuous shape functions to the 
pressure space improves diffusivity and interfaces approximation. A 
complementary approach is the introduction of a Distributed Lagrangian 
Multiplier. In this approach a DLM is introduced to the kinematic 
condition. The role of the DLM is to implicitly load the fluid with the 
elastic contribution. Numerical and theoretical evidence show that the 
scheme is unconditionally stable. Moreover the scheme shows encouraging 
performances in terms of diffusivity and robustness.


Venue: SISSA, lecture room 133 at 2 pm on Monday 15 December