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- W2016553692 abstract "We introduce in this paper an algorithm for integration of the transport-diffusion equations by combining the Galerkin finite element method with the discretization of the total derivative along the characteristics. The present algorithm is an extension of the one proposed by the author [R. Bermejo, Numer. Math., 60 (1991), pp. 163–194] to integrate the transport equation. The algorithm consists of a convective–diffusive splitting of the equations along the characteristics. Such a scheme permits an efficient evaluation of inner products of functions that take their values in different partitions (grids). The convective stage of the splitting is evaluated in a $Q_1 $-conforming finite element space, while the diffusive stage can be approximated in higher-order ($Q_2 $ or $Q_3 $) finite element spaces. We analyze two time-discretization schemes for the diffusive stage, namely, the backward Euler and Crank–Nicolson schemes. Our $L^2 $-norm estimate shows that, provided $h = O(Delta t)$, the backward Euler scheme combined with a $Q_1 $-conforming finite element yields optimal error estimates, whereas the Crank–Nicolson scheme is optimal when combined with a $Q_2 $-conforming finite element." @default.
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- W2016553692 title "A Galerkin-Characteristic Algorithm for Transport-Diffusion Equations" @default.
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- W2016553692 doi "https://doi.org/10.1137/0732018" @default.
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