Based on the Kirchhoff transformation and the natural boundary element method, we investigate a coupled natural boundary element method and finite element method for quasi-linear problems in a bounded or unbounded dom...Based on the Kirchhoff transformation and the natural boundary element method, we investigate a coupled natural boundary element method and finite element method for quasi-linear problems in a bounded or unbounded domain with a concave angle. By the principle of the natural boundary reduction, we obtain natural integral equation on circular arc artificial boundaries, and get the coupled variational problem and its numerical method. Moreover, the convergence of approximate solutions and error estimates are obtained. Finally, some numerical examples are presented to show the feasibility of our method. Our work can be viewed as an extension of the existing work of H.D. Han et al..展开更多
In this paper, we investigate an overlapping domain decomposition algorithm for elliptic boundary value problems over an infinite domain with concave angles.The algorithm is constructed, and its convergence is discuss...In this paper, we investigate an overlapping domain decomposition algorithm for elliptic boundary value problems over an infinite domain with concave angles.The algorithm is constructed, and its convergence is discussed. The finite element method and natural boundary element are alternatively applied to solve a bounded subdomain and a typical unbounded subdomain. It has overcome the difficulty met in standard domain decomposition method for problems with unbounded domains.The convergence rate is analysed in details for a typical domain. Finally, some numerical example are presented to show effectiveness of our method.展开更多
基金Acknowledgments. We would like to thank the reviewers for their valuable comments which improve the paper. This research is partly supported by the National Natural Science Foundation of China contact/grant number： 11071109 Foundation for Innovative Program of Jiangsu Province, contact/grant number： CXZZ12_0383 and CXZZ11_0870.
文摘Based on the Kirchhoff transformation and the natural boundary element method, we investigate a coupled natural boundary element method and finite element method for quasi-linear problems in a bounded or unbounded domain with a concave angle. By the principle of the natural boundary reduction, we obtain natural integral equation on circular arc artificial boundaries, and get the coupled variational problem and its numerical method. Moreover, the convergence of approximate solutions and error estimates are obtained. Finally, some numerical examples are presented to show the feasibility of our method. Our work can be viewed as an extension of the existing work of H.D. Han et al..
文摘In this paper, we investigate an overlapping domain decomposition algorithm for elliptic boundary value problems over an infinite domain with concave angles.The algorithm is constructed, and its convergence is discussed. The finite element method and natural boundary element are alternatively applied to solve a bounded subdomain and a typical unbounded subdomain. It has overcome the difficulty met in standard domain decomposition method for problems with unbounded domains.The convergence rate is analysed in details for a typical domain. Finally, some numerical example are presented to show effectiveness of our method.
