A Hybrid High-Order method for Kirchhoff-Love plate bending problems
It provides a novel discretization for fourth-order elliptic problems with high-order accuracy on polygonal meshes, benefiting computational mechanics researchers.
This paper introduces a Hybrid High-Order (HHO) method for Kirchhoff-Love plate bending problems, achieving convergence rates of h^{k+1} in energy norm and h^{k+3} in L^2 norm for polynomial degree k≥1, validated by numerical experiments.
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.