Anisotropic mesh adaption in Computational Fluid Dynamics: application to the advection-diffusion-reaction and the Stokes problems

MOX 15

Anisotropic mesh adaption in Computational Fluid Dynamics: application to the advection-diffusion-reaction and the Stokes problems

Wednesday 5th March 2003

Formaggia, Luca; Micheletti, Stefano; Perotto, Simona

In this work we develop an anisotropic a posteriori error analysis of the advection-diffusion-reaction and the Stokes problems. This is the first step towards the study of more complex situation, such as the Oseen and Navier-Stokes equations, which are very common in Computational Fluid Dynamic (CFD) applications. The leading idea of our analysis consists in combining the anisotropic interpolation error estimates for affine triangular finite element provided in [14,15] with a posteriori error analysis based on a dual problem associated with the problem at hand [6,34]. Anisotropic interpolation estimates take into account more in detail the geometry of the triangular elements, i.e. not just their diameter but also their aspect ratio and orientation. Ont he other hand, the introduction of the dual problem allows us to control suitable functionals of the discretization error, e.g. the lift and drag around bodies in external flows, mean and local values, etc. The combined use of both approaches yelds an adaptive algorithm which, via an iterative process, can be used for designing the optimal mesh for the problem at hand

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Formaggia, L.; Micheletti, S.; Perotto, S., Anisotropic mesh adaption in Computational Fluid Dynamics: application to the advection-diffusion-reaction and the Stokes problems, Appl. Numer. Math., 51 (2004), no. 4, 511-533