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Article Dans Une Revue Applied Numerical Analysis and Computational Mathematics Année : 2016

On optimal simplicial 3D meshes for minimizing the Hessian-based errors

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Youssef Mesri
Mehdi Khalloufi
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Elie Hachem

Résumé

In this paper we derive a multi-dimensional mesh adaptation method which produces optimal meshes for quadratic functions, positive semi-definite. The method generates anisotropic adaptive meshes as quasi-uniform ones in some metric space, with the tensor metric being computed based on interpolation error estimates. It does not depend, a priori, on the PDEs at hand in contrast to residual methods. The estimated error is then used to steer local modifications of the mesh in order to reach a prescribed level of error in LpLp-norm or a prescribed number of elements. The LpLp-norm of the estimated error is then minimized in order to get an optimal mesh. Numerical examples in 2D and 3D for analytic challenging problems and an application to a Computational Fluid Dynamics problem are presented and discussed in order to show how the proposed method recovers optimal convergence rates as well as to demonstrate its computational performance.
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Dates et versions

hal-01354332 , version 1 (18-08-2016)

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Youssef Mesri, Mehdi Khalloufi, Elie Hachem. On optimal simplicial 3D meshes for minimizing the Hessian-based errors. Applied Numerical Analysis and Computational Mathematics, 2016, 109, pp.235-249. ⟨10.1016/j.apnum.2016.07.007⟩. ⟨hal-01354332⟩
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