A non-separable progressive multivariate WENO-2r point value
arxiv(2024)
摘要
The weighted essentially non-oscillatory technique using a stencil of 2r
points (WENO-2r) is an interpolatory method that consists in obtaining a
higher approximation order from the non-linear combination of interpolants of
r+1 nodes. The result is an interpolant of order 2r at the smooth parts and
order r+1 when an isolated discontinuity falls at any grid interval of the
large stencil except at the central one. Recently, a new WENO method based on
Aitken-Neville's algorithm has been designed for interpolation of equally
spaced data at the mid-points and presents progressive order of accuracy close
to discontinuities. This paper is devoted to constructing a general progressive
WENO method for non-necessarily uniformly spaced data and several variables
interpolating in any point of the central interval. Also, we provide explicit
formulas for linear and non-linear weights and prove the order obtained.
Finally, some numerical experiments are presented to check the theoretical
results.
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