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Texas A&M University
Mathematics

Numerical Analysis Seminar

Spring 2023

 

Date:January 12, 2023
Time:3:00pm
Location:BLOC 302
Speaker:Andreas Veeser, Università di Milano
Title:Tree approximation with conforming meshes
Abstract:

Consider approximants over conforming (or face-to-face) meshes that are generated by means of bisection of simplices. Then the tree approximation algorithms by Binev and DeVore (2004) and Binev (2018) construct near best approximants with quasi-optimal complexity. Doing so, the decisions in the algorithm do not take into account the requirement of conformity. This entails that the near best constant depends on the completion process which turns a nonconforming mesh into a conforming one.

We shall generalize the tree approximation algorithm form Binev (2018) to take into account the conformity of the generated meshes, thereby avoiding the aforementioned dependence.


Date:March 22, 2023
Time:3:00pm
Location:BLOC 302
Speaker:Dr Francis Aznaran, University of Oxford
Title:Finite element methods for the Stokes–Onsager–Stefan–Maxwell equations of multicomponent flow
Abstract:The Onsager framework for linear irreversible thermodynamics provides a thermodynamically consistent model of mass transport in a phase consisting of multiple species, via the Stefan–Maxwell equations, but a complete description of the overall transport problem necessitates also solving the momentum equations for the flow velocity of the medium. We derive a novel nonlinear variational formulation of this coupling, called the (Navier–)Stokes–Onsager–Stefan–Maxwell system, which governs molecular diffusion and convection within a non-ideal, single-phase fluid composed of multiple species, in the regime of low Reynolds number in the steady state. We propose an appropriate Picard linearisation posed in a novel Sobolev space relating to the diffusional driving forces, and prove convergence of a structure-preserving finite element discretisation. This represents some of the first rigorous numerics for the coupling of multicomponent molecular diffusion with compressible convective flow. The broad applicability of our theory is illustrated with simulations of the centrifugal separation of noble gases and the microfluidic mixing of hydrocarbons.