**Commenced**in January 2007

**Frequency:**Monthly

**Edition:**International

**Paper Count:**30458

##### Mechanical Quadrature Methods and Their Extrapolations for Solving First Kind Boundary Integral Equations of Anisotropic Darcy-s Equation

**Authors:**
Xin Luo,
Jin Huang,
Chuan-Long Wang

**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:**
Extrapolation Methods,
anisotropic,
Darcy's equation,
mechanical quadrature methods,
a posteriori error estimate

**Digital Object Identifier (DOI):**
doi.org/10.5281/zenodo.1329032

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