Related papers: A Hybrid High-Order method for Kirchhoff-Love plat…
We devise and analyze two hybrid high-order (HHO) methods for the numerical approximation of the biharmonic problem. The methods support polyhedral meshes, rely on the primal formulation of the problem, and deliver $O(h^{k+1})$ $H^2$-error…
In this article, we design and analyze a hybrid high-order (HHO) finite element approximation for the solution of a nonlocal nonlinear problem of Kirchhoff type. The HHO method involves arbitrary-order polynomial approximations on…
We devise a Hybrid High-Order (HHO) method for highly oscillatory elliptic problems that is capable of handling general meshes. The method hinges on discrete unknowns that are polynomials attached to the faces and cells of a coarse mesh;…
In this work, we develop and analyze a Hybrid High-Order (HHO) method for steady non-linear Leray-Lions problems. The proposed method has several assets, including the support for arbitrary approximation orders and general polytopal meshes.…
We devise and analyze $C^0$-conforming hybrid high-order (HHO) methods to approximate biharmonic problems with either clamped or simply supported boundary conditions. $C^0$-conforming HHO methods hinge on cell unknowns which are…
We devise and evaluate numerically a Hybrid High-Order (HHO) method for incremental associative plasticity with small deformations. The HHO method uses as discrete unknowns piecewise polynomials of order $k\ge1$ on the mesh skeleton,…
This chapter provides an introduction to Hybrid High-Order (HHO) methods. These are new generation numerical methods for PDEs with several advantageous features: the support of arbitrary approximation orders on general polyhedral meshes,…
We devise and evaluate numerically Hybrid High-Order (HHO) methods for hyperelastic materials undergoing finite deformations. The HHO methods use as discrete unknowns piecewise polynomials of order $k\ge1$ on the mesh skeleton, together…
We devise and evaluate numerically a Hybrid High-Order (HHO) method for finite plasticity within a logarithmic strain framework. The HHO method uses as discrete unknowns piecewise polynomials of order $k\ge1$ on the mesh skeleton, together…
We propose a novel hybrid high-order method (HHO) to approximate singularly perturbed fourth-order PDEs on domains with a possibly curved boundary. The two key ideas in devising the method are the use of a Nitsche-type boundary penalty…
The relaxation in the calculus of variation motivates the numerical analysis of a class of degenerate convex minimization problems with non-strictly convex energy densities with some convexity control and two-sided $p$-growth. The…
In this work, we study the design and analysis of a novel hybrid high-order (HHO) method on unfitted meshes. HHO methods rely on a pair of unknowns, combining polynomials attached to the mesh faces and the mesh cells. In the unfitted…
A new approach is introduced for deriving a mixed variational formulation for Kirchhoff plate bending problems with mixed boundary conditions involving clamped, simply supported, and free boundary parts. Based on a regular decomposition of…
We are concerned in designing a suitable numerical scheme based on the equal-order hybrid high-order (HHO) method for the linear parabolic integro-differential equations. The spatial discretization is made using the equal-order HHO method…
In this work, we develop a fully implicit Hybrid High-Order algorithm for the Cahn-Hilliard problem in mixed form. The space discretization hinges on local reconstruction operators from hybrid polynomial unknowns at elements and faces. The…
This paper presents the design and analysis of a Hybrid High-Order (HHO) approximation for a distributed optimal control problem governed by the Poisson equation. We propose three distinct schemes to address unconstrained control problems…
This paper proposes a new hybrid high-order discretization for the biharmonic problem and the corresponding eigenvalue problem. The discrete ansatz space includes degrees of freedom in $n-2$ dimensional submanifolds (e.g., nodal values in…
In this article, we design and analyze a Hybrid High-Order (HHO) finite element approximation for a class of strongly nonlinear boundary value problems. We consider an HHO discretization for a suitable linearized problem and show its…
In this work we develop a novel fully discrete version of the plates complex, an exact Hilbert complex relevant for the mixed formulation of fourth-order problems. The derivation of the discrete complex follows the discrete de Rham…
We design a Hybrid High-Order (HHO) scheme for the Poisson problem that is fully robust on polytopal meshes in the presence of small edges/faces. We state general assumptions on the stabilisation terms involved in the scheme, under which…