Journal
INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING
Volume 60, Issue 1, Pages 255-281Publisher
WILEY
DOI: 10.1002/nme.961
Keywords
finite calculus; computational mechanics; stabilized methods; finite element method; incompressible flow; incompressible solids; strain localization
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The expression 'finite calculus' refers to the derivation of the governing differential equations in mechanics by invoking balance of fluxes, forces, etc. in a space-time domain of finite size. The governing equations resulting from this approach are different from those of infinitesimal calculus theory and they incorporate new terms which depend on the dimensions of the balance domain. The new governing equations allow the derivation of naturally stabilized numerical schemes using any discretization procedure. The paper discusses the possibilities of the finite calculus method for the finite element solution of convection-diffusion problems with sharp gradients, incompressible fluid flow and incompressible solid mechanics problems and strain localization situations. Copyright (C) 2004 John Wiley Sons, Ltd.
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