High degree discontinuous Petrov-Galerkin immersed finite element methods using fictitious elements for elliptic interface problems

[摘要] 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). (C) 2018 Elsevier B.V. All rights reserved.

[发布日期] 2019-12-15

[效力级别]  Proceedings Paper

[关键词] Interface problems;Immersed finite element spaces;Higher degree;Fictitious element;Discontinuous Petrov-Galerkin method