Mixed discontinuous Legendre wavelet Galerkin method for solving elliptic partial differential equations

Abstract

By incorporating the Legendre multiwavelet into the mixed discontinuous Galerkin method, in this paper, we present a novel method for solving second-order elliptic partial differential equations (PDEs), which is known as the mixed discontinuous Legendre multiwavelet Galerkin 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. The proposed method is also applicable to some other kinds of PDEs.

Keywords:

• elliptic partial differential equation
• discontinuous Galerkin method
• Wavelet–Galerkin method
• mixed discontinuous Wavelet–Galerkin method
• Legendre multiwavelet

2010 AMS Subject Classifications :

• 65D99
• 65N99
• 41A25
• 44A45

Acknowledgements

The authors are grateful to the editor and the referees for their valuable comments that greatly improved the quality of this paper. This work is supported by NSFC (Grant No. 10771227) and NCET-05-0759.