Discontinuous Legendre wavelet element method for elliptic partial differential equations |
| |
Authors: | Xiaoyang Zheng Xiaofan YangHong Su Liqiong Qiu |
| |
Affiliation: | a College of Mathematics and Statistics, Chongqing University, Chongqing 400030, China b College of Computer Science, Chongqing University, Chongqing 400030, China c College of Mathematics and Statistics, Chongqing University of Technology, Chongqing 400050, China |
| |
Abstract: | By incorporating the Legendre multiwavelet into the discontinuous Galerkin (DG) method, this paper presents a novel approach for solving Poisson’s equation with Dirichlet boundary, which is known as the discontinuous Legendre multiwavelet element (DLWE) method, derive an adaptive algorithm for the method, and estimate the approximating error of its numerical fluxes. One striking advantage of our method is that the differential operator, boundary conditions and numerical fluxes involved in the elementwise computation can be done with lower time cost. Numerical experiments demonstrate the validity of this method. Furthermore, this paper generalizes the DLWE method to the general elliptic equations defined on a bounded domain and describes the possibilities of constructing optimal adaptive algorithm. The proposed method and its generalizations are also applicable to some other kinds of partial differential equations. |
| |
Keywords: | Elliptic partial differential equation Discontinuous Galerkin method Wavelet-Galerkin method Bounded domain Legendre multiwavelet |
本文献已被 ScienceDirect 等数据库收录! |
|