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A higher order method based on local maximum entropy approximation
Author(s) -
González David,
Cueto Elías,
Doblaré Manuel
Publication year - 2010
Publication title -
international journal for numerical methods in engineering
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.421
H-Index - 168
eISSN - 1097-0207
pISSN - 0029-5981
DOI - 10.1002/nme.2855
Subject(s) - mathematics , tensor product , quadratic equation , spline (mechanical) , spline interpolation , quartic function , boundary value problem , smoothness , mathematical analysis , mathematical optimization , pure mathematics , geometry , engineering , statistics , structural engineering , bilinear interpolation
We present here a generalization of local maximum entropy (max‐ent) approximation for high orders of consistency (i.e. quadratic, cubic, …). The method is based upon the application of the de Boor's algorithm to the standard, linear local max‐ent approximation. The resulting approximation possesses some interesting properties, such as non‐negativity, ∞ smoothness, exact interpolation on the boundary and variation diminishing (no Gibbs effect). The resulting structure has many similarities with B‐spline surfaces, but without the tensor‐product structure typical of that approximation. Examples are provided of its use in the framework of a Galerkin method showing the potential of the proposed method in solving boundary value problems. Copyright © 2010 John Wiley & Sons, Ltd.