کد مقاله | کد نشریه | سال انتشار | مقاله انگلیسی | نسخه تمام متن |
---|---|---|---|---|
6933634 | 867752 | 2013 | 20 صفحه PDF | دانلود رایگان |
عنوان انگلیسی مقاله ISI
Weak Galerkin methods for second order elliptic interface problems
دانلود مقاله + سفارش ترجمه
دانلود مقاله ISI انگلیسی
رایگان برای ایرانیان
موضوعات مرتبط
مهندسی و علوم پایه
مهندسی کامپیوتر
نرم افزارهای علوم کامپیوتر
پیش نمایش صفحه اول مقاله
![عکس صفحه اول مقاله: Weak Galerkin methods for second order elliptic interface problems Weak Galerkin methods for second order elliptic interface problems](/preview/png/6933634.png)
چکیده انگلیسی
Weak Galerkin methods refer to general finite element methods for partial differential equations (PDEs) in which differential operators are approximated by their weak forms as distributions. Such weak forms give rise to desirable flexibilities in enforcing boundary and interface conditions. A weak Galerkin finite element method (WG-FEM) is developed in this paper for solving elliptic PDEs with discontinuous coefficients and interfaces. Theoretically, it is proved that high order numerical schemes can be designed by using the WG-FEM with polynomials of high order on each element. Extensive numerical experiments have been carried out to validate the WG-FEM for solving second order elliptic interface problems. High order of convergence is numerically confirmed in both L2 and Lâ norms for the piecewise linear WG-FEM. Special attention is paid to solve many interface problems, in which the solution possesses a certain singularity due to the nonsmoothness of the interface. A challenge in research is to design nearly second order numerical methods that work well for problems with low regularity in the solution. The best known numerical scheme in the literature is of order O(h) to O(h1.5) for the solution itself in Lâ norm. It is demonstrated that the WG-FEM of the lowest order, i.e., the piecewise constant WG-FEM, is capable of delivering numerical approximations that are of order O(h1.75) to O(h2) in the Lâ norm for C1 or Lipschitz continuous interfaces associated with a C1 or H2 continuous solution.
ناشر
Database: Elsevier - ScienceDirect (ساینس دایرکت)
Journal: Journal of Computational Physics - Volume 250, 1 October 2013, Pages 106-125
Journal: Journal of Computational Physics - Volume 250, 1 October 2013, Pages 106-125
نویسندگان
Lin Mu, Junping Wang, Guowei Wei, Xiu Ye, Shan Zhao,