High order Lagrange-Galerkin methods for the conservative formulation of the advection-diffusion equation
High order Lagrange-Galerkin methods for the conservative formulation of the advection-diffusion equation
"High order Lagrange-Galerkin methods for the conservative formulation of the advection-diffusion equation", organizado por CITMAga. Será impartido por Rodolfo Bermejo da Universidad Politécnica de Madrid.
Data: mércores 20 de decembro de 2023
Hora: 10:00 h.
Duración: 1 hora
Lugar: Aula Magna da Facultade de Matemáticas, ou ben online a través do enlace Teams meeting. Conferenciante por Teams.
Abstract:
In this talk I present the numerical analysis of high order both in time and space Lagrange-Galerkin methods for the conservative formulation of the advection-diffusion equation. As time discretization scheme we consider the Backward Differentiation Formulas up to order q = 5. The development and analysis of the methods are performed in the framework of time evolving finite elements presented in C. M. Elliot and T. Ranner, IMA Journal of Numerical Analysis 41, 1696-1845 (2021). The error estimates show through their dependence on the parameters of the equation the existence of different regimes in the behavior of the numerical solution; namely, in the diffusive regime, that is, when the diffusion parameter 𝜇 is large, the error is
, whereas in the advective regime, 𝜇 ≪ 1, the convergence is
It is worth remarking that the error constant does not have exponential 𝜇−1 dependence.