# A Hybrid High-Order method for Kirchhoff-Love plate bending problems

## TL;DR

This paper introduces a new Hybrid High-Order method for accurately solving fourth-order Kirchhoff-Love plate bending problems on polygonal meshes, with proven convergence and robustness supported by numerical tests.

## Contribution

The paper develops a novel HHO discretization supporting arbitrary orders and polygonal meshes, with proven convergence and error estimates for plate bending problems.

## Key findings

- Convergence rate of h^{k+1} in energy norm
- Error estimate of h^{k+3} in L^2 norm under regularity
- Numerical experiments confirm robustness and accuracy

## 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 energy 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.