A Hybrid High-Order method for Kirchhoff–Love plate bending problemsReport as inadecuate

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1 Dipartimento di Matematica -Francesco Brioschi- Laboratorio di Modellistica e Calcolo Scientifico MOX 2 IMAG - Institut Montpelliérain Alexander Grothendieck 3 LMS - Laboratoire de mécanique des solides

Abstract : We present a novel Hybrid High-Order HHO discretization of fourth-order elliptic problems arising from the mechanical modeling of the bending behavior of Kirchhoff-Love plates, including the biharmonic equation as a particular case. The proposed HHO method supports arbitrary approximation orders on general polygonal meshes, and reproduces the key mechanical equilibrium relations locally inside each element. When polynomials of degree $k\ge 1$ are used as unknowns, we prove convergence in $h^{k+1}$ with $h$ denoting, as usual, the meshsize in an energy-like norm. A key ingredient in the proof are novel approximation results for the oblique biharmonic projector on local polynomial spaces. Under biharmonic regularity assumptions, a sharp estimate in $h^{k+3}$ is also derived for the $L^2$-norm of the error on the deflection. The theoretical results are supported by numerical experiments, which additionally show the robustness of the method with respect to the choice of the stabilization.

Keywords : oblique biharmonic projector Hybrid High-Order methods Kirchhoff–Love plates biharmonic problems

Author: Francesco Bonaldi - Daniele Di Pietro - Giuseppe Geymonat - Françoise Krasucki -

Source: https://hal.archives-ouvertes.fr/


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