arXiv subjects

Cuiyu He

Publications and source records attributed to Cuiyu He.

20 records · Page 2Linked to original sources

arXiv2016

Finite Element Methods for Interface Problems: Robust Residual-Based A Posteriori Error Estimates

For elliptic interface problems, this paper studies residual-based a posteriori error estimations for various finite element approximations. For the conforming and the Raviart-Thomas mixed elements in two-dimension and for the Crouzeix-Raviart nonconforming and the discontinuous Galerkin elements in both two- and three-dimensions, the global reliability bounds are established with constants independent of the jump of the diffusion coefficient. Moreover, we obtain these estimates with no assumption on the distribution of the diffusion coefficient.

math.NA↗

arXiv2016

Residual-based a Posteriori Error Estimate for Interface Problems: Nonconforming Linear Elements

In this paper, we study a modified residual-based a posteriori error estimator for the nonconforming linear finite element approximation to the interface problem. The reliability of the estimator is analyzed by a new and direct approach without using the Helmholtz decomposition. It is proved that the estimator is reliable with constant independent of the jump of diffusion coefficients across the interfaces, without the assumption that the diffusion coefficient is quasi-monotone. Numerical results for one test problem with intersecting interfaces are also presented.

math.NA↗