TY - JFULL AU - Xin Luo and Jin Huang and Chuan-Long Wang PY - 2012/9/ TI - Mechanical Quadrature Methods and Their Extrapolations for Solving First Kind Boundary Integral Equations of Anisotropic Darcy-s Equation T2 - International Journal of Mathematical and Computational Sciences SP - 1156 EP - 1160 VL - 6 SN - 1307-6892 UR - https://publications.waset.org/pdf/766 PU - World Academy of Science, Engineering and Technology NX - Open Science Index 68, 2012 N2 - The mechanical quadrature methods for solving the boundary integral equations of the anisotropic Darcy-s equations with Dirichlet conditions in smooth domains are presented. By applying the collectively compact theory, we prove the convergence and stability of approximate solutions. The asymptotic expansions for the error show that the methods converge with the order O (h3), where h is the mesh size. Based on these analysis, extrapolation methods can be introduced to achieve a higher convergence rate O (h5). An a posterior asymptotic error representation is derived in order to construct self-adaptive algorithms. Finally, the numerical experiments show the efficiency of our methods. ER -