Abstract
A meshless, barycentric interpolation collocation method for numerical approximation of Darcy flows is proposed. The barycentric Lagrange interpolation and its differentiation matrices are basic tool to discretize governing equations, Dirichlet and Neumann boundary conditions. For Darcy flows in irregular domains, embedding the irregular domain into a rectangular, the barycentric interpolation collocation method can be directly applied. The resultant saddle-point systems come from combining the discretized governing equations and boundary conditions, such that we can deal easy with all kinds of boundary condition either regular or irregular domains. Some numerical examples are given to illustrate the accuracy, stability and robust of presented method.
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