Residual distribution and applications to kinetic models
Date:
In this talk, we will understand the residual distribution (RD) as a framework in which various classical numerical methods can be viewed (finite volume, finite elements and discontinuous Galerkin). Moreover, we will see how this can help understanding the connections between these classical schemes as well as easily creating new families of schemes. Indeed, though the classical description of the Residual Distribution is linked to continuous Finite Element, we will show that they are equivalent to some Finite Volume schemes and, conversely, that Finite Volume schemes can be written into RD. Finally, we will apply RD to some kinetic models that approximates hyperbolic conservation laws (Euler and SW equations).
References Abgrall, Rémi. “Some remarks about conservation for residual distribution schemes.” Computational Methods in Applied Mathematics 18.3 (2018): 327-351. Abgrall, Rémi, and Davide Torlo. “High order asymptotic preserving deferred correction implicit-explicit schemes for kinetic models.” SIAM Journal on Scientific Computing 42.3 (2020): B816-B845.