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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