Excellence in Research and Innovation for Humanity

Xin Luo

Publications

2

Publications

2
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.

Keywords:
Darcy's equation, anisotropic, mechanical quadrature methods, extrapolation methods, a posteriori error estimate.
1
17077
Mechanical Quadrature Methods for Solving First Kind Boundary Integral Equations of Stationary Stokes Problem
Abstract:

By means of Sidi-Israeli’s quadrature rules, mechanical quadrature methods (MQMs) for solving the first kind boundary integral equations (BIEs) of steady state Stokes problem are presented. The convergence of numerical solutions by MQMs is proved based on Anselone’s collective compact and asymptotical compact theory, and the asymptotic expansions with the odd powers of the errors are provided, which implies that the accuracy of the approximations by MQMs possesses high accuracy order O (h3). Finally, the numerical examples show the efficiency of our methods.

Keywords:
Stokes problem, boundary integral equation, mechanical quadrature methods, asymptotic expansions.