Tuesday, August 23, 2022 - 14:00 in V2-210/216
Finite element approximation and weak- strong uniqueness for incompressible heat-conducting fluids
A talk in the BI.discrete Workshop series by
Pablo Alexei Gazca Orozco from Prague
| Abstract: |
In this talk, I will present some results in connection with a system describing an incompressible power-law-like heat-conducting fluid, and convergence of finite element approximations. I will discuss how various notions of weak solutions can be more or less amenable to analysis, depending on the value of the power-law exponent. In particular, in the context of low power-law exponents, I will introduce the notion of a dissipative weak solution of the system and highlight the connections and differences to the existing approaches in the literature. A feature of this notion of solution is that the solution satisfies a weak-strong uniqueness principle; moreover, since the solutions are constructed via a finite element approximation, this leads (almost, not quite) to the first numerical convergence result for the full system including viscous dissipation. This work was done in collaboration with V. Patel (Oxford).
Within the CRC this talk is associated to the project(s): B7 |
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