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Finite Element Characteristic Methods Requiring no Quadrature

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Abstract

The characteristic methods are known to be very efficient for convection-diffusion problems including the Navier-Stokes equations. Convergence is established when the integrals are evaluated exactly, otherwise there are even cases where divergence has been shown to happen. The family of methods studied here applies Lagrangian convection to the gradients and the function as in Yabe (Comput. Phys. Commun. 66(2–3), 233–242, 1991); the method does not require an explicit knowledge of the equation of the gradients and can be applied whenever the gradients of the convection velocity are known numerically. We show that converge can be second order in space or more. Applications are given for the rotating bell problem.

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  1. LJLL, Université Pierre et Marie Curie, Place Jussieu, Paris, 75005, France

    Olivier Pironneau

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  1. Olivier Pironneau
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Correspondence to Olivier Pironneau.

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In honor of M. Tabata for his sixtieth birthday.

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Pironneau, O. Finite Element Characteristic Methods Requiring no Quadrature. J Sci Comput 43, 402–415 (2010). https://doi.org/10.1007/s10915-009-9276-2

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  • DOI: https://doi.org/10.1007/s10915-009-9276-2

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