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766
Mechanical Quadrature Methods and Their Extrapolations for Solving First Kind Boundary Integral Equations of Anisotropic Darcy-s Equation
Abstract:
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.
Digital Article Identifier (DAI):

References:

[1] Mera, N.S., Elliott, L., Ingham, D.B., Lesnic, D.: A comparison of boundary element method formulations for steady state anisotropic heat conduction problems. Engineering Analysis with Boundary Elements. 25, 115-128 (2001)
[2] Muskat, M. :1946, The Flow of Homogeneous Fluids through Porous Media, J. Edwards(ed.), Ann Arbor, Michigan.
[3] A. Sidi and M. Israeli, Quadrature methods for periodic singular and weakly singular Fredholm integral equation, J. Sci. Comput., 3 (1988), 201-231.
[4] X. -M. He and T. L¨u, A finite element splitting extrapolation for second order hyperbolic equations, SIAM J. Sci. Comput., 31 (2009), 4244- 4265.
[5] J. Saranen and I. Sloan, Quadrature methods for logarithmic-kernel integral equations on closed curves, IMA J. Numer. Anal., 12 (1992), 167-187.
[6] Y. Yan and I. Sloan, On integral equations of the first kind with logarithmic kernels, J. Integral Equations Appl., 1 (1988), 517-548.
[7] M. Costabel, V. J. Ervin and E. P. Stephan, On the convergence of collocation methods for Symm-s integral equation on open curves. Math. Comp., 51 (1988), 167-179.
[8] P. Davis, Methods of Numerical Integration. Second edition, Academic Press, New York, 1984.
[9] J. Huang and Z. Wang, Extrapolation algorithms for solving mixed boundary integral equations of the Helmholtz equation by mechanical quadrature methods. SIAM J. SCI Comput. Vol. 31. No. 6, pp. 4115- 4129.
[10] F. Chatelin, Spectral Approximation of Linear Operator, Academic Press, New York, 1983.
[11] K. Atkinson, The Numerical Solution of Integral Equations of the Second Kind, Cambridge University Press, Cambridge, UK, 1997.
[12] J. Huang and T. L¨u, The mechanical quadrature methods and their extrapolation for solving BIE of Steklov eigenvalue problems, J. Comput. Math., 22 (2004), pp. 719-726.
[13] I. H. Sloan and A. Spence, The Galerkin method for integral equations of first-kind with logarithmic kernel: theory, IMA J. Numer. Anal., 8 (1988), 105-122.
[14] J. Huang, L¨u, Z.C., Li, The mechanical quadrature methods and their splitting extrapolation for boundary integral equations of first kind on open contours, Appl Numer Math 2009; 59: 2908-22.

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