Flux-equilibrated based a posteriori error analysis for an interface problem with CutFEM
This work addresses an incremental improvement in error estimation for interface problems in computational mathematics, benefiting researchers in numerical analysis and finite element methods.
The paper tackles the problem of local recovery of conservative fluxes and a posteriori error analysis for an elliptic interface problem with discontinuous coefficients, achieving sharp reliability of the error estimator as demonstrated in a numerical experiment.
This paper addresses the local recovery of conservative fluxes and the a posteriori error analysis for an elliptic interface problem with discontinuous coefficients. The transmission conditions on the interface are imposed by means of Nitsche's method and the discretization is carried out using conforming finite elements on unfitted meshes via the CutFEM method. A flux is subsequently defined in the global Raviart-Thomas space, ensuring that it satisfies the natural conservation property on the cut cells, and is then employed in the a posteriori error analysis. We prove here the sharp reliability of the error estimator and show a numerical experiment which illustrates the approach.