Some analytical results for an algebraic flux correction scheme for a steady convection-diffusion equation in 1D

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Date
2014
Volume
1916
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Publisher
Berlin : Weierstraß-Institut für Angewandte Analysis und Stochastik
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Abstract

Algebraic flux correction schemes are nonlinear discretizations of convection dominated problems. In this work, a scheme from this class is studied for a steady-state convection-diffusion equation in one dimension. It is proved that this scheme satisfies the discrete maximum principle. Also, as it is a nonlinear scheme, the solvability of the linear subproblems arising in a Picard iteration is studied, where positive and negative results are proved. Furthermore, the non-existence of solutions for the nonlinear scheme is proved by means of counterexamples. Therefore, a modification of the method, which ensures the existence of a solution, is proposed. A weak version of the discrete maximum principle is proved for this modified method.

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Keywords
Finite element method, convection-diffusion equation, algebraic flux correction, discrete maximum principle, fixed point iteration, solvability of linear subproblems, solvability of nonlinear problem
Citation
Barrenechea, G. R., John, V., & Knobloch, P. (2014). Some analytical results for an algebraic flux correction scheme for a steady convection-diffusion equation in 1D (Vol. 1916). Vol. 1916. Berlin : Weierstraß-Institut für Angewandte Analysis und Stochastik.
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