Very high-order finite volume method for one-dimensional convection diffusion problems

Stéphane Clain (1, 2) , Steven Diot (1) , Raphaël Loubère (1) , Gaspar Machado (2) , Rui Ralha (3) , Rui M. S. Pereira (4)

1 IMT - Institut de Mathématiques de Toulouse UMR5219
2 DMA - Departamento de Matemática e Aplicaçoes
3 DMA - Departamento de Matemática e Aplicações
4 DMA - Departamento de Matemática e Aplicações

We propose a new finite volume method to provide very high-order accuracy for the convection diffusion problem. The main tool is a polynomial reconstruction baesd on the mean values to provide the optimal order. Numerical examples are proposed to show the method efficiency.

Mots clés: finite volume; very high-order; convection diffusion; polynomial reconstruction

Domaines: Analyse numérique [math.NA]

Stéphane Clain, Steven Diot, Raphaël Loubère, Gaspar Machado, Rui Ralha, et al.. Very high-order finite volume method for one-dimensional convection diffusion problems. 2011. ⟨hal-00630204⟩