8 papers · 1 filter
Optimal error estimates for non-conforming approximations of linear parabolic problems with minimal regularity
J Droniou, R Eymard, T Gallouët +2
We consider a general linear parabolic problem with extended time boundary conditions (including initial value problems and periodic ones), and approximate it by the implicit Euler…
Exact pressure elimination for the Crouzeix-Raviart scheme applied to the Stokes and Navier-Stokes problems
Eric Chénier, Robert Eymard
We show that, using the Crouzeix-Raviart scheme, a cheap algebraic transformation, applied to the coupled velocity-pressure linear systems issued from the transient or steady Stoke…
Non-conforming finite elements on polytopal meshes
Jerome Droniou, Robert Eymard, Thierry Gallouet +1
In this work we present a generic framework for non-conforming finite elements on polytopal meshes, characterised by elements that can be generic polygons/polyhedra. We first prese…
Uniform-in-time convergence of numerical methods for non-linear degenerate parabolic equations
Jerome Droniou, Robert Eymard
Gradient schemes is a framework that enables the unified convergence analysis of many numerical methods for elliptic and parabolic partial differential equations: conforming and no…
A Class of Collocated Finite Volume Schemes for Incompressible Flow Problems
R. Eymard, R. Herbin, J. -C Latché +1
In this paper, we present a class of finite volume schemes for incompressible flow problems. The unknowns are collocated at the center of the control volumes, and the stability of…
Galerkin approximation of linear problems in Banach and Hilbert spaces
Wolfgang Arendt, Isabelle Chalendar, Robert Eymard
In this paper we study the conforming Galerkin approximation of the problem: find u U such that a(u, v) = <L, v> for all v V, where U and V are Hilbert or Banach spaces…