Numerical solution of Poisson equation with wavelet bases of Hermite cubic splines on the interval

• Published in: Applied mathematics and mechanics Vol. 30; no. 10; pp. 1325 - 1334
• Main Authors: Xiang, Jia-wei, Chen, Xue-feng, Li, Xi-kui
• Format: Journal Article
• Language: English
• Published: Heidelberg Shanghai University Press 01.10.2009; State Key Laboratory for Manufacturing Systems Engineering, Xi'an Jiaotong University,Xi'an 710049, P. R. China%State Key Laboratory for Manufacturing Systems Engineering, Xi'an Jiaotong University,Xi'an 710049, P. R. China%State Key Laboratory of Structural Analysis for Industrial Equipment, Dalian University of Technology, Dalian 116024, P. R. China; Faculty of Mechanical and Electrical Engineering, Guilin University of Electronic Technology,Guilin 541004, P. R. China
• Subjects: Applications of Mathematics; Approximation; Classical Mechanics; Finite element method; Fluid- and Aerodynamics; Intervals; Mathematical analysis; Mathematical Modeling and Industrial Mathematics; Mathematical models; Mathematics; Mathematics and Statistics; Partial Differential Equations; Poisson equation; Splines; Wavelet; 65L05; O351.2; 35F30; Poisson equation; wavelet-based finite element method; Hermite cubic spline wavelet; 65T60; lifting scheme
• ISSN: 0253-4827; 1573-2754
• DOI: 10.1007/s10483-009-1012-x

A new wavelet-based finite element method is proposed for solving the Poisson equation. The wavelet bases of Hermite cubic splines on the interval are employed as the multi-scale interpolation basis in the finite element analysis. The lifting scheme of the wavelet-based finite element method is discussed in detail. For the orthogonal characteristics of the wavelet bases with respect to the given inner product, the corresponding multi-scale finite element equation can be decoupled across scales, totally or partially, and suited for nesting approximation. Numerical examples indicate that the proposed method has the higher efficiency and precision in solving the Poisson equation.