Stella Krell

Benchmark 3D: a version of the DDFV scheme with cell/vertex unknowns on general meshes

This paper gives numerical results for a 3D extension of the 2D DDFV scheme. Our scheme is of the same inspiration as the one called CeVe-DDFV ([9]), with a more straightforward dual mesh construction. We sketch the construction in which, starting from a given 3D mesh (which can be non conformal and have arbitrary polygonal faces), one defines a dual mesh and a diamond mesh, reconstructs a discrete gradient, and proves the discrete duality property. Details can be found in [1].

A Hybrid High-Order method for the steady incompressible Navier--Stokes problem

In this work we introduce and analyze a novel Hybrid High-Order method for the steady incompressible Navier–Stokes equations. The proposed method is inf-sup stable on general polyhedral meshes, supports arbitrary approximation orders, and is (relatively) inexpensive thanks to the possibility of statically condensing a subset of the unknowns at each nonlinear iteration. We show under general assumptions the existence of a discrete solution, which is also unique provided a data smallness condition is verified. Using a compactness argument, we prove convergence of the sequence of discrete solutions to minimal regularity exact solutions for general data. For more regular solutions, we prove optimal convergence rates for the energy-norm of the velocity and the

Stabilized DDFV Schemes For The Incompressible Navier-Stokes Equations

L^2

DDFV Ventcell Schwarz Algorithms

L2-norm of the pressure under a standard data smallness assumption. More precisely, when polynomials of degree

Simulations of non homogeneous viscous flows with incompressibility constraints

k\ge 0

On 3D DDFV discretization of gradient and divergence operators. I. Meshing, operators and discrete duality.

k≥0 at mesh elements and faces are used, both quantities are proved to converge as