Simon Lemaire: Thursday, 13th March 2025 at 10:30
Abstract: Within the last 20 years or so, a myriad of novel numerical approaches, capable of accommodating general polytopal meshes, have pop up in the literature. The main purpose of this talk is to tidy up the room, and to build connections, in the context of a model variable diffusion problem, between these different approaches. Our study will focus on skeletal methods. As opposed to plain-vanilla finite volume and discontinuous Galerkin discretizations, skeletal methods essentially attach degrees of freedom to the mesh skeleton. Our study will discriminate between primal and mixed formulations of the problem at hand. Somewhat unsurprisingly, we will see that, at the end of the day, all these approaches fall within only two distinct approximation paradigms.
