3 papers
math.NA2024
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…
math.NA2023
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…
math.NA2023
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…