On the construction of second-to-fourth-order accurate approximations of spatial derivatives on an arbitrary set of points
D. A. Shirobokov
Dorodnicyn Computing Center, Russian Academy of Sciences,
ul. Vavilova 40, Moscow, 119991, Russia
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.
Poisson's equation, biharmonic equation, meshless methods, approximation of spatial derivatives.
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Computational Mathematics and Mathematical Physics, 2006, 46:6, 1023–1043
D. A. Shirobokov, “On the construction of second-to-fourth-order accurate approximations of spatial derivatives on an arbitrary set of points”, Zh. Vychisl. Mat. Mat. Fiz., 46:6 (2006), 1074–1095; Comput. Math. Math. Phys., 46:6 (2006), 1023–1043
Citation in format AMSBIB
\paper On the construction of second-to-fourth-order accurate approximations of spatial derivatives on an arbitrary set of points
\jour Zh. Vychisl. Mat. Mat. Fiz.
\jour Comput. Math. Math. Phys.
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