KMS Of Academy of mathematics and systems sciences, CAS
New error estimates of Adini's elements for Poisson's equation | |
Huang, HT; Li, ZC; Yan, NN | |
2004-07-01 | |
Source Publication | APPLIED NUMERICAL MATHEMATICS |
ISSN | 0168-9274 |
Volume | 50Issue:1Pages:49-74 |
Abstract | In this paper, we report some new discoveries of Adini's elements for Poisson's equation in error estimates, stability analysis and global superconvergence. It is well known that the optimal convergence rate \\u - u(/1)\\(1) = O(h(3)\u\(4)) can be obtained, where u(/1) and u are the Adini's solution and the true solution, respectively. In this paper, for all kinds of boundary conditions of Poisson's equations, the supercloseness parallel tou(I)(A)-u(/1)parallel to = O(h(3.5)parallel touparallel to(5)) can be obtained for uniform rectangles rectangle(ij), where u A is the Adini's interpolation of the true solution u. Moreover, for the Neumann problems of Poisson's equation, new treatments adding the explicit natural constraints (u(n))(ij) = g(ij) on the boundary are proposed to yield the Adini's solution u(ji)* having supercloseness parallel tou(I)(A) - u* parallel to(I) = O(h(4)parallel touparallel to(5)). Hence, the global superconvergence parallel tou - Pi(5)u(h)(*) = O(h(4)parallel touparallel to(5)) can be achieved, where Pi5u(h)(*) is an a posteriori interpolant of polynomials with order five based on the obtained solution u*. New basic estimates of errors are derived for Adini's elements. Numerical experiments in this paper are also provided to verify the supercloseness and superconvergences, O(h(3.5)) and O(h(4)), and the standard condition number O(h(-2)). It is worthy pointing out that for the Neumann problems on rectangular domains, the traditional finite element method is not as good as the newly proposed method interpolating the Neumann condition in this paper. Not only is the new method more accurate, but also economical in computation, as the discrete system has less unknowns. (C) 2003 IMACS. Published by Elsevier B.V. All rights reserved. |
Keyword | Adini's elements Neumann problems Poisson's equation global superconvergence stability analysis |
DOI | 10.1016/j.apnum.2003.10.009 |
Language | 英语 |
WOS Research Area | Mathematics |
WOS Subject | Mathematics, Applied |
WOS ID | WOS:000221648600003 |
Publisher | ELSEVIER SCIENCE BV |
Citation statistics | |
Document Type | 期刊论文 |
Identifier | http://ir.amss.ac.cn/handle/2S8OKBNM/19520 |
Collection | 中国科学院数学与系统科学研究院 |
Affiliation | 1.Natl Sun Yat Sen Univ, Dept Appl Math, Kaohsiung 80424, Taiwan 2.Acad Sinica, Acad Math & Syst Sci, Inst Syst Sci, Beijing 100080, Peoples R China |
Recommended Citation GB/T 7714 | Huang, HT,Li, ZC,Yan, NN. New error estimates of Adini's elements for Poisson's equation[J]. APPLIED NUMERICAL MATHEMATICS,2004,50(1):49-74. |
APA | Huang, HT,Li, ZC,&Yan, NN.(2004).New error estimates of Adini's elements for Poisson's equation.APPLIED NUMERICAL MATHEMATICS,50(1),49-74. |
MLA | Huang, HT,et al."New error estimates of Adini's elements for Poisson's equation".APPLIED NUMERICAL MATHEMATICS 50.1(2004):49-74. |
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