MIB Galerkin method for elliptic interface problems
文献类型：期刊论文
| 作者 | Xia, Kelin1,2; Zhan, Meng2; Wei, Guo-Wei1,3 |
| 刊名 | JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS
 |
| 出版日期 | 2014-12-15 |
| 卷号 | 272页码:195-220 |
| 关键词 | Finite element method Galerkin formulation Matched interface and boundary Elliptic equations Discontinuous coefficients |
| 英文摘要 | Material interfaces are omnipresent in the real-world structures and devices. Mathematical modeling of material interfaces often leads to elliptic partial differential equations (PDEs) with discontinuous coefficients and singular sources, which are commonly called elliptic interface problems. The development of high-order numerical schemes for elliptic interface problems has become a well defined field in applied and computational mathematics and attracted much attention in the past decades. Despite of significant advances, challenges remain in the construction of high-order schemes for nonsmooth interfaces, i.e., interfaces with geometric singularities, such as tips, cusps and sharp edges. The challenge of geometric singularities is amplified when they are associated with low solution regularities, e.g., tip-geometry effects in many fields. The present work introduces a matched interface and boundary (MIB) Galerkin method for solving two-dimensional (2D) elliptic PDEs with complex interfaces, geometric singularities and low solution regularities. The Cartesian grid based triangular elements are employed to avoid the time consuming mesh generation procedure. Consequently, the interface cuts through elements. To ensure the continuity of classic basis functions across the interface, two sets of overlapping elements, called MIB elements, are defined near the interface. As a result, differentiation can be computed near the interface as if there is no interface. Interpolation functions are constructed on MIB element spaces to smoothly extend function values across the interface. A set of lowest order interface jump conditions is enforced on the interface, which in turn, determines the interpolation functions. The performance of the proposed MIB Galerkin finite element method is validated by numerical experiments with a wide range of interface geometries, geometric singularities, low regularity solutions and grid resolutions. Extensive numerical studies confirm the designed second order convergence of the MIB Galerkin method in the L-infinity and L-2 errors. Some of the best results are obtained in the present work when the interface is C-1 or Lipschitz continuous and the solution is C-2 continuous. (C) 2014 Elsevier B.V. All rights reserved. |
| WOS标题词 | Science & Technology ; Physical Sciences |
| 类目[WOS] | Mathematics, Applied |
| 研究领域[WOS] | Mathematics |
| 关键词[WOS] | FINITE-ELEMENT-METHOD ; EMBEDDED BOUNDARY METHOD ; FICTITIOUS DOMAIN METHOD ; NAVIER-STOKES EQUATIONS ; MATCHED INTERFACE ; DISCONTINUOUS COEFFICIENTS ; IRREGULAR DOMAINS ; CONVERGENCE ANALYSIS ; 3 DIMENSIONS ; MAXWELLS EQUATIONS |
| 收录类别 | SCI |
| 语种 | 英语 |
| WOS记录号 | WOS:000340336600015 |
| 公开日期 | 2015-07-14 |
| 源URL | [http://ir.wipm.ac.cn/handle/112942/1302]  |
| 专题 | 武汉物理与数学研究所_理论与交叉研究部 |
| 作者单位 | 1.Michigan State Univ, Dept Math, E Lansing, MI 48824 USA 2.Chinese Acad Sci, Wuhan Inst Phys & Math, Wuhan 430071, Peoples R China 3.Michigan State Univ, Dept Elect & Comp Engn, E Lansing, MI 48824 USA |
| 推荐引用方式 GB/T 7714 | Xia, Kelin,Zhan, Meng,Wei, Guo-Wei. MIB Galerkin method for elliptic interface problems[J]. JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS,2014,272:195-220. |
| APA | Xia, Kelin,Zhan, Meng,&Wei, Guo-Wei.(2014).MIB Galerkin method for elliptic interface problems.JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS,272,195-220. |
| MLA | Xia, Kelin,et al."MIB Galerkin method for elliptic interface problems".JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS 272(2014):195-220. |
入库方式： OAI收割
来源：武汉物理与数学研究所
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