Conditioning of a Hybrid High-Order Scheme on Meshes with Small Faces

A hybrid multilevel method for high-order discretization of the Euler equations on unstructured meshes

Article history: Received 23 June 2009 Received in revised form 25 January 2010 Accepted 25 January 2010 Available online 4 February 2010

A high-order cell-centered Lagrangian scheme for two-dimensional compressible fluid flows on unstructured meshes

We present a high-order cell-centered Lagrangian scheme for solving the two-dimensional gas dynamics equations on unstructured meshes. A node-based discretization of the numerical fluxes for the physical conservation laws allows to derive a scheme that is compatible with the geometric conservation law (GCL). Fluxes are computed using a nodal solver which can be viewed as a two-dimensional exten...

High Order Fluctuation Schemes on Triangular Meshes

We develop a new class of schemes for the numerical solution of first-order steady conservation laws. The schemes are of the residual distribution, or fluctuation-splitting type. These schemes have mostly been developed in the context of triangular or tetrahedral elements whose degrees of freedom are their nodal values. We work here with more general elements that allow high-order accuracy. We ...

High Order Edge Elements on Simplicial Meshes

Low order edge elements are widely used for electromagnetic field problems. Higher order edge approximations are receiving increasing interest but their definition become rather complex. In this paper we propose a simple definition for Whitney edge elements of polynomial degree higher than one. We give a geometrical localization of all degrees of freedom over particular edges and provide a basi...

A Unifying High-Order Method for the Navier-Stokes Equations on Hybrid Unstructured Meshes