On the construction of second-to-fourth-order accurate approximations of spatial derivatives on an arbitrary set of points |
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Authors: | D. A. Shirobokov |
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Affiliation: | (1) Dorodnicyn Computing Center, Russian Academy of Sciences, ul. Vavilova 40, Moscow, 119991, Russia |
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Abstract: | The method of undetermined coefficients generates a set of fixed-order approximations of spatial derivatives on an irregular stencil. An additional condition is proposed that singles out a unique scheme from this set. The resulting second-to-fourth order accurate approximations are applied to solving Poisson’s and the biharmonic equations. The bending of a plate supported by an edge, the nonlinear bending of a circular plate, and two-dimensional problems in solid mechanics are discussed. A method is proposed for constructing oriented approximations, which are validated by solving an advection equation. |
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Keywords: | Poisson’ s equation biharmonic equation meshless methods approximation of spatial derivatives |
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