The hybrid high-order method for polytopal meshes
DA Di Pietro, J Droniou - Number 19 in Modeling, Simulation and …, 2020 - Springer
Originally introduced in [146, 158], Hybrid High-Order (HHO) methods provide a framework
for the discretisation of models based on Partial Differential Equations (PDEs) with features …
for the discretisation of models based on Partial Differential Equations (PDEs) with features …
A review on arbitrarily regular conforming virtual element methods for second-and higher-order elliptic partial differential equations
The virtual element method is well suited to the formulation of arbitrarily regular Galerkin
approximations of elliptic partial differential equations of order 2 p 1, for any integer p 1≥ 1 …
approximations of elliptic partial differential equations of order 2 p 1, for any integer p 1≥ 1 …
Divergence free virtual elements for the Stokes problem on polygonal meshes
In the present paper we develop a new family of Virtual Elements for the Stokes problem on
polygonal meshes. By a proper choice of the Virtual space of velocities and the associated …
polygonal meshes. By a proper choice of the Virtual space of velocities and the associated …
hp-version discontinuous Galerkin methods on polygonal and polyhedral meshes
A Cangiani, EH Georgoulis… - Mathematical Models and …, 2014 - World Scientific
An hp-version interior penalty discontinuous Galerkin method (DGFEM) for the numerical
solution of second-order elliptic partial differential equations on general computational …
solution of second-order elliptic partial differential equations on general computational …
A review of hybrid high-order methods: formulations, computational aspects, comparison with other methods
DA Di Pietro, A Ern, S Lemaire - … and challenges in modern approaches to …, 2016 - Springer
Abstract Hybrid High-Order (HHO) methods are formulated in terms of discrete unknowns
attached to mesh faces and cells (hence, the term hybrid), and these unknowns are …
attached to mesh faces and cells (hence, the term hybrid), and these unknowns are …
A Hybrid High-Order method for Leray–Lions elliptic equations on general meshes
D Di Pietro, J Droniou - Mathematics of Computation, 2017 - ams.org
In this work, we develop and analyze a Hybrid High-Order (HHO) method for steady
nonlinear Leray–Lions problems. The proposed method has several assets, including the …
nonlinear Leray–Lions problems. The proposed method has several assets, including the …
An -conforming virtual element for Darcy and Brinkman equations
G Vacca - Mathematical Models and Methods in Applied …, 2018 - World Scientific
The focus of this paper is on developing a virtual element method (VEM) for Darcy and
Brinkman equations. In [L. Beirão da Veiga, C. Lovadina and G. Vacca, ESAIM Math. Model …
Brinkman equations. In [L. Beirão da Veiga, C. Lovadina and G. Vacca, ESAIM Math. Model …
[图书][B] Generalized barycentric coordinates in computer graphics and computational mechanics
In Generalized Barycentric Coordinates in Computer Graphics and Computational
Mechanics, eminent computer graphics and computational mechanics researchers provide …
Mechanics, eminent computer graphics and computational mechanics researchers provide …
[HTML][HTML] Agglomeration of polygonal grids using graph neural networks with applications to multigrid solvers
Agglomeration-based strategies are important both within adaptive refinement algorithms
and to construct scalable multilevel algebraic solvers. In order to automatically perform …
and to construct scalable multilevel algebraic solvers. In order to automatically perform …
Discontinuous Galerkin approximation of flows in fractured porous media on polytopic grids
We present a numerical approximation of Darcy's flow through a fractured porous medium
which employs discontinuous Galerkin methods on polytopic grids. For simplicity, we …
which employs discontinuous Galerkin methods on polytopic grids. For simplicity, we …