Possibilities of finite calculus in computational mechanics

ABSTRACT The expression “finite calculus” refers to the derivation of the governing differential equations in mechanics by invoking balance of fluxes, forces, etc. in a domain of finite size. The governing equations resulting from this approach are different from those of infinitessimal calculus theory and they incorporate new terms depending on the dimensions of the balance domain. The new modified equations allow to derive naturally stabilized numerical schemes using finite element, finite difference, finite volume or meshless methods. The paper briefly discusses the possibilities of the modified governing equations derived via the finite calculus technique for the numerical solution of convection-diffusion problems, incompressible flow and incompressible solid mechanic problems and strain localization problems.

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