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math.NA2026
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…
math.NA2025
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…
math.NA2024
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…