Colloquium: "A Hitchhiker's Guide to the Virtual Element Method for Elliptic Interface Problems"

Abstract: At the International Congress of Mathematicians 2014, Franco Brezzi, as one of the visionary founding fathers of the finite element method, introduced a new class of methods called virtual element method (VEM) to approximate elliptic PDEs. VEM can be viewed as an apparent extension of the finite element method from simplicial/tensorial to polytopal meshes. In this talk, I shall tell  the stories of my collaborators and I, as "hitchhikers", trying to decode and dissect the deeper essence of VEM. A new set of sufficient geometric conditions is studied for VEM to achieve the optimal order of convergence. This new set of conditions lays a theoretical foundation of a simple adaptive mesh refinement strategy on polytopal meshes, which facilitates the approximation of elliptic interface problems by VEM on body-fitted meshes. Lastly, we will talk about a recent result on using the VEM meta-framework to bridge the partially-penalized immersed interface finite element to the body-fitted finite element when approximating a model interface problem.

Host: Renato Feres

Tea will be served @ 3:30pm in room 200.