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

Abstract : 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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https://hal-mines-paristech.archives-ouvertes.fr/hal-01354332
Contributor : Magalie Prudon <>
Submitted on : Thursday, August 18, 2016 - 3:34:10 PM
Last modification on : Wednesday, December 9, 2020 - 2:42:08 PM

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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, Wiley-VCH Verlag: No OnlineOpen, 2016, 109, pp.235-249. ⟨10.1016/j.apnum.2016.07.007⟩. ⟨hal-01354332⟩

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