7 papers
The eXtended Virtual Element Method for elliptic problems with weakly singular solutions
Jerome Droniou, Gianmarco Manzini, Liam Yemm
This paper introduces a novel eXtended virtual element method, an extension of the conforming virtual element method. The XVEM is formulated by incorporating appropriate enrichment…
An enriched hybrid high-order method for the Stokes problem with application to flow around submerged cylinders
Liam Yemm
An enriched hybrid high-order method is designed for the Stokes equations of fluid flow and is fully applicable to generic curved meshes. Minimal regularity requirements of the enr…
A new approach to handle curved meshes in the hybrid high-order method
Liam Yemm
The hybrid high-order method is a modern numerical framework for the approximation of elliptic PDEs. We present here an extension of the hybrid high-order method to meshes possessi…
A hybrid high-order scheme for the stationary, incompressible magnetohydrodynamics equations
Jérôme Droniou, Liam Yemm
We propose and analyse a hybrid high-order (HHO) scheme for stationary incompressible magnetohydrodynamics equations. The scheme has an arbitrary order of accuracy and is applicabl…
Conditioning of a Hybrid High-Order scheme on meshes with small faces
Santiago Badia, Jerome Droniou, Liam Yemm
We conduct a condition number analysis of a Hybrid High-Order (HHO) scheme for the Poisson problem. We find the condition number of the statically condensed system to be independen…
Design and analysis of the Extended Hybrid High-Order method for the Poisson problem
Liam Yemm
We propose an Extended Hybrid High-Order scheme for the Poisson problem with solution possessing weak singularities. Some general assumptions are stated on the nature of this singu…
Robust Hybrid High-Order method on polytopal meshes with small faces
Jerome Droniou, Liam Yemm
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 th…