6 papers
A posteriori error estimates for mixed finite element discretization of the multigroup Neutron Simplified Transport equations with Robin boundary condition
Patrick Ciarlet, Minh-Hieu Do, Mario Gervais +1
We analyse a posteriori error estimates for the discretization with mixed finite elements on simplicial or Cartesian meshes of the multigroup neutron simplified transport (SPN ) eq…
Adaptive mesh refinement on Cartesian meshes applied to the mixed finite element discretization of the multigroup neutron diffusion equations
Patrick Ciarlet, Minh-Hieu Do, François Madiot
The multigroup neutron diffusion equations are often used to model the neutron density at the nuclear reactor core scale. Classically, these equations can be recast in a mixed vari…
Crouzeix-Raviart elements on simplicial meshes in dimensions
Nis-Erik Bohne, Patrick Ciarlet, Stefan Sauter
In this paper we introduce Crouzeix-Raviart elements of general polynomial order and spatial dimension for simplicial finite element meshes. We give explicit represent…
A Family of Crouzeix-Raviart Finite Elements in 3D
Patrick Ciarlet, Charles F. Dunkl, Stefan A. Sauter
In this paper we will develop a family of non-conforming "Crouzeix-Raviart" type finite elements in three dimensions. They consist of local polynomials of maximal degree $p\in\math…
The Fourier Singular Complement Method for the Poisson problem. Part II: axisymmetric domains
Patrick Ciarlet, Beate Jung, Samir Kaddouri +2
This paper is the second part of a threefold article, aimed at solving numerically the Poisson problem in three-dimensional prismatic or axisymmetric domains. In the first part of…
The Fourier Singular Complement Method for the Poisson problem. Part I: prismatic domains
Patrick Ciarlet, Beate Jung, Samir Kaddouri +2
This is the first part of a threefold article, aimed at solving numerically the Poisson problem in three-dimensional prismatic or axisymmetric domains. In this first part, the Four…