Sibson and non-Sibsonian interpolants for elliptic partial differential equations
نویسنده
چکیده
The Natural Element Method (NEM) is a meshless Galerkin method which has shown promise in the area of computational mechanics. In earlier applications of NEM [1–3], natural neighbor (Sibson) coordinates [4] were used to construct the trial and test functions. Recently, Belikov and co-workers [5] proposed a new interpolation scheme (non-Sibsonian interpolation) based on natural neighbors. In this paper, we present the Sibson and the non-Sibsonian interpolants, and discuss their use in a Galerkin scheme for the solution of elliptic PDEs. In particular, by choosing the non-Sibsonian interpolant, the exact imposition of essential boundary conditions in a meshless method is realized.
منابع مشابه
Natural neighbour Galerkin methods
Natural neighbour co-ordinates (Sibson co-ordinates) is a well-known interpolation scheme for multivariate data tting and smoothing. The numerical implementation of natural neighbour co-ordinates in a Galerkin method is known as the natural element method (NEM). In the natural element method, natural neighbour co-ordinates are used to construct the trial and test functions. Recent studies on NE...
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