Cuiyu He, University of Texas Rio Grande Valley
Authors: Cuiyu He and Daniela Capatina
2022 AWM Research Symposium
Women in Numerical Analysis and Scientific Computing

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.

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