A posteriori error estimates for mixed finite element discretization of the multigroup Neutron Simplified Transport equations with Robin boundary condition
This work addresses error estimation for neutron transport simulations, which is crucial for nuclear engineering applications, but it is incremental as it builds on existing methods for specific boundary conditions.
The authors developed a posteriori error estimates for mixed finite element discretizations of multigroup neutron simplified transport equations with Robin boundary conditions, providing guaranteed and locally efficient estimators, and extended the approach to domain decomposition methods with adaptive mesh refinement, as validated by numerical experiments.
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 ) equations, in the case where a Robin (or Fourier type) boundary condition is imposed on the boundary. This boundary condition is of particular importance in neutronics, since it corresponds to the well-known vacuum boundary condition. We provide guaranteed and locally efficient estimators. In particular, a specific estimator is designed to handle the Robin boundary condition. We also develop the theory in the case of mixed imposed boundary conditions, of Dirichlet, Neumann or Fourier type. The approach is further extended to a Domain Decomposition Method, the so-called DD+L 2 jumps method. In this framework, the adaptive mesh refinement strategy is implemented for a discretization using Cartesian meshes on each subdomain. Numerical experiments illustrate the theory.