Splitting extrapolation algorithms for solving the boundary integral equations of anisotropic Darcy's equation on polygons by mechanical quadrature methods

Authors:
Xin Luo;Jin Huang;Chuan-Long Wang
Affiliations:
School of Mathematical Sciences, University of Electronic Science and Technology of China, Chengdu, People's Republic of China 611731;School of Mathematical Sciences, University of Electronic Science and Technology of China, Chengdu, People's Republic of China 611731;Department of Mathematics, Taiyuan Normal University, Taiyuan, People's Republic of China 030012
Venue:
Numerical Algorithms
Year:
2013

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Abstract

In this paper we study the stability and convergence of the solution for the first kind integral equations of the anisotropic Darcy's equations by the mechanical quadrature methods on closed polygonal boundaries in 驴2. Using the collectively compact theory, we construct numerical solutions which converge with the order $O\;(h^{3}_{\text{max}})$ , where $h_{\text{max}}$ is the mesh size. In addition, An a posteriori asymptotic error representation is derived by splitting extrapolation methods in order to construct self-adaptive algorithms, and the convergence rate $O\;(h^{5}_{\text{max}})$ can be achieved after using the splitting extrapolation methods once. Finally, the numerical examples show the efficiency of our methods.