We aim to recover locally conservative and $H(div)$ conforming fluxes for the linear Cut Finite Element Solution with Nitsche's method for Poisson problems with Dirichlet boundary condition. The computation of the conservative flux in the Raviart-Thomas space is completely local and does not require to solve any mixed problem. The $L^2$-norm of the difference between the numerical flux and the recovered flux can then be used as a posteriori error estimator in the adaptive mesh refinement procedure. Theoretically we are able to prove the global reliability and local efficiency. The theoretical results are verified in the numerical results.
equilibrate flux recovery for cut finite element method
Cuiyu He, University of Texas Rio Grande ValleyAuthors: Cuiyu He and Daniela Capatina
2022 AWM Research Symposium
Women in Numerical Analysis and Scientific Computing