arXiv subjects

Hailong Guo

Publications and source records attributed to Hailong Guo.

40 records · Page 3Linked to original sources

arXiv2016

Gradient recovery for elliptic interface problem: II. immersed finite element methods

This is the second paper on the study of gradient recovery for elliptic interface problem. In our previous work [H. Guo and X. Yang, 2016, arXiv:1607.05898], we developed gradient recovery finite element method based on body-fitted mesh. In this paper, we propose new gradient recovery methods based on two immersed interface finite element methods: symmetric and consistent immersed finite method [H. Ji, J. Chen and Z. Li, J. Sci. Comput., 61 (2014), 533--557] and Petrov-Galerkin immersed finite element method [T.Y. Hou, X.-H. Wu and Y. Zhang, Commun. Math. Sci., 2 (2004), 185--205, and S. Hou and X.-D. Liu, J. Comput. Phys., 202 (2005), 411--445]. Compared to body-fitted mesh based gradient recover methods, immersed finite element methods provide a uniform way of recovering gradient on regular meshes. Numerical examples are presented to confirm the superconvergence of both gradient recovery methods. Moreover, they provide asymptotically exact a posteriori error estimators for both immersed finite element methods.

math.NA↗

arXiv2016

Gradient recovery for elliptic interface problem: I. body-fitted mesh

In this paper, we propose a novel gradient recovery method for elliptic interface problem using body-fitted mesh in two dimension. Due to the lack of regularity of solution at interface, standard gradient recovery methods fail to give superconvergent results, and thus will lead to overrefinement when served as a posteriori error estimator. This drawback is overcome by designing an immersed gradient recovery operator in our method. We prove the superconvergence of this method for both mildly unstructured mesh and adaptive mesh, and present several numerical examples to verify the superconvergence and its robustness as a posteriori error estimator.

math.NA↗

arXiv2014

Superconvergent Two-grid Methods For Elliptic Eigenvalue Problems

Some numerical algorithms for elliptic eigenvalue problems are proposed, analyzed, and numerically tested. The methods combine advantages of the two-grid algorithm, two-space method, the shifted inverse power method, and the polynomial preserving recovery technique . Our new algorithms compare favorably with some existing methods and enjoy superconvergence property.

math.NA↗

arXiv2014

Hessian Recovery for Finite Element Methods

In this article, we propose and analyze an effective Hessian recovery strategy for the Lagrangian finite element of arbitrary order $k$. We prove that the proposed Hessian recovery preserves polynomials of degree $k+1$ on general unstructured meshes and superconverges at rate $O(h^k)$ on mildly structured meshes. In addition, the method preserves polynomials of degree $k+2$ on translation invariant meshes and produces a symmetric Hessian matrix when the sampling points for recovery are selected with symmetry. Numerical examples are presented to support our theoretical results.

math.NA↗