Volume 52, Number 2, March–April 2018
|Page(s)||393 - 421|
|Published online||29 May 2018|
A Hybrid High-Order method for Kirchhoff–Love plate bending problems★
MOX, Dipartimento di Matematica, Politecnico di Milano,
2 Institut Montpelliérain Alexander Grothendieck, CNRS, Univ. Montpellier, Montpellier, France
3 LMS, Ecole Polytechnique, CNRS, Université Paris-Saclay, 91128 Palaiseau, France
* Corresponding author: email@example.com
Accepted: 26 December 2017
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 ≥ 1 are used as unknowns, we prove convergence in hk+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 energy projector on local polynomial spaces. Under biharmonic regularity assumptions, a sharp estimate in hk+3 is also derived for the L2-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.
Mathematics Subject Classification: 65N30 / 65N12 / 74K20
Key words: Hybrid High-Order methods / Kirchhoff–Love plates / biharmonic problems / energy projector
The work of the first author was supported by Agence Nationale de la Recherche projects HHOMM (ANR-15-CE40-0005), along with the second author, and ARAMIS (ANR-12-BS01-0021), along with the third and fourth authors; also, it was partially supported by SIR Research Grant no. RBSI14VTOS funded by MIUR – Italian Ministry of Education, Universities and Research.
© EDP Sciences, SMAI 2018
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