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• W2893679803 abstract "We propose a new strategy for constructing the pth degree immersed finite element (IFE) spaces by applying the least squares framework in Adjerid et al. (2017) on fictitious elements. This new construction method significantly reduces the ill-conditioning, caused by the small subelement issue in Adjerid et al. (2017), of solving the local IFE shape functions. The proposed IFE spaces are employed in a discontinuous Petrov–Galerkin (DPG) scheme to solve the second order elliptic interface problems. We present a group of numerical examples to show that the DPGIFE method with the new pth degree IFE space as the trial function space has the optimal convergence rate, which improves the numerical results reported in Adjerid et al. (2017)." @default.
• W2893679803 created "2018-10-05" @default.
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• W2893679803 date "2019-12-01" @default.
• W2893679803 modified "2023-09-28" @default.
• W2893679803 title "High degree discontinuous Petrov–Galerkin immersed finite element methods using fictitious elements for elliptic interface problems" @default.
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• W2893679803 doi "https://doi.org/10.1016/j.cam.2018.09.028" @default.
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