Matrix decomposition algorithms for arbitrary order C0 tensor product finite element systems

JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS

卷:275

Article

Du, Kui¹  Fairweather, Graeme²  Sun, Weiwei³ 

[1] Xiamen Univ, Sch Math Sci, Xiamen 361005, Peoples R China

[2] Amer Math Soc, Ann Arbor, MI 48103 USA

[3] City Univ Hong Kong, Dept Math, Kowloon, Hong Kong, Peoples R China

关键词: Poisson's equation;    Finite element Galerkin method;    C-0 piecewise polynomials;    Matrix decomposition algorithms;   

DOI  :  10.1016/j.cam.2014.08.015

来源: Elsevier

【 摘 要 】

Matrix decomposition algorithms (MDAs) are fast direct methods for the solution of systems of linear algebraic equations which arise in the approximation of Poisson's equation on the unit square using various techniques such as finite difference, spline collocation and spectral methods. The attraction of MDAs is that they employ fast Fourier transforms and require O(N-2 log N) operations on an N x N uniform partition of the unit square. In this paper, MDAs are formulated for the solution of the finite element Galerkin equations arising when spaces of C-0 piecewise polynomials of degree k >= 3 are employed. Results of numerical experiments exhibit the expected optimal global convergence rates and super-convergence phenomena. (C) 2014 Elsevier B.V. All rights reserved.

【 授权许可】

Free