Design of an Essentially Non-Oscillatory Reconstruction Procedure on Finite-Element Type Meshes
作者： Remi Abgrall
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摘要: In this report, we have designed an Essentially Non Oscillatory reconstruction for functions defined on finite-element type meshes. Two related problems are studied: The interpolation of possibility unsmooth multivariate arbitrary meshes and the a function from its averages in control volumes surrounding nodes mesh. Concerning first problem, studied behaviour highest coefficients two polynomials interpolations that may admit discontinuities locally regular curves: Lagrange approximation such mean polynomial any volume is equal to be approximated. This enables us choose best stencil approximation. choice smallest possible number stencils addressed. methods been one based adaptation so-called via deconvolution method irregular second lies as above. conservative up quadrature formula exactly conservative. expected order accuracy, but much less expensive than one. Some numerical examples given which demonstrate efficiency reconstruction.
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