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Blurred derivatives and meshless methods
Author(s) -
Pardo Enrique
Publication year - 2002
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.567
Subject(s) - polygon mesh , mathematics , poisson's equation , partial differential equation , regularized meshless method , implementation , computer science , mathematical optimization , finite element method , mathematical analysis , geometry , singular boundary method , physics , boundary element method , thermodynamics , programming language
In this work we first introduce and describe the concept of blurred derivatives. It is shown how they can be used both to approximate differential equations and to re‐express them in alternative ways. In particular, formulations in terms of functional integrals can be obtained using blurred derivatives and extended to non‐linear problems. Blurred derivatives are shown to provide higher flexibility for selection of approximation functions than strong and weak formulations. Some computational implementations of one‐dimensional problems are discussed and the relationship between several well‐known numerical methods is analysed. Finally a meshless numerical scheme for the Poisson equation is described in detail. Its performance is compared with linear finite elements and generalized finite differences on unstructured meshes of points. Copyright © 2002 John Wiley & Sons, Ltd.