ABSTRACT
In this paper, we consider the numerical solution of the three-dimensional axisymmetric anisotropic Darcy's equation with Dirichlet boundary conditions. By the potential theory and the indirect boundary element methods, we transform the system to be a one-dimensional boundary integral equation. The mechanical quadrature method (MQM) is developed to solve the integral equation. Moreover, the errors of MQM have a multivariate asymptotic expansion with the order of for all mesh widths . Once discrete equations are solved in parallel, the accuracy of numerical approximations can be improved to be the order of by splitting extrapolation algorithm. Moreover, a posteriori asymptotic error estimate is derived to construct self-adaptive algorithms.
Disclosure statement
No potential conflict of interest was reported by the authors.
Funding
This work was supported by the National Natural Science Foundation of China [grant number 11371079].