Flux recovery for Cut Finite Element Method and its application in <i>a posteriori</i> error estimation

Capatina, Daniela; He, Cuiyu

doi:10.1051/m2an/2021071

Flux recovery for Cut Finite Element Method and its application in a posteriori error estimation

Capatina, Daniela ; He, Cuiyu

ESAIM: Mathematical Modelling and Numerical Analysis , Tome 55 (2021) no. 6, pp. 2759-2784

Résumé

In this article, 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 L²-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 also prove the global reliability and local efficiency. The theoretical results are verified in the numerical results. Moreover, in the numerical results we also observe optimal convergence rate for the flux error.

MR

DOI : 10.1051/m2an/2021071

Classification : 68Q25, 68R10, 68U05
Keywords: CutFEM, $$ error estimation, flux recovery, adaptive mesh refinement

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     author = {Capatina, Daniela and He, Cuiyu},
     title = {Flux recovery for {Cut} {Finite} {Element} {Method} and its application in \protect\emph{a posteriori} error estimation},
     journal = {ESAIM: Mathematical Modelling and Numerical Analysis },
     pages = {2759--2784},
     year = {2021},
     publisher = {EDP-Sciences},
     volume = {55},
     number = {6},
     doi = {10.1051/m2an/2021071},
     mrnumber = {4344863},
     language = {en},
     url = {https://www.numdam.org/articles/10.1051/m2an/2021071/}
}

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Capatina, Daniela; He, Cuiyu. Flux recovery for Cut Finite Element Method and its application in a posteriori error estimation. ESAIM: Mathematical Modelling and Numerical Analysis , Tome 55 (2021) no. 6, pp. 2759-2784. doi: 10.1051/m2an/2021071

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