Some analytical results for an algebraic flux correction scheme for a steady convection-diffusion equation in one dimension
Barrenechea, Gabriel and Volker, John and Knobloch, Petr (2014) Some analytical results for an algebraic flux correction scheme for a steady convection-diffusion equation in one dimension. IMA Journal of Numerical Analysis. ISSN 0272-4979
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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.
Creators(s): |
Barrenechea, Gabriel ![]() | Item type: | Article |
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ID code: | 50863 |
Keywords: | finite element method, solvability of nonlinear problem, solvability of linear subproblems, fixed point iteration, discrete maximum principle, algebraic flux correction, convection-diffusion equation, Probabilities. Mathematical statistics, Computational Mathematics, Applied Mathematics, Mathematics(all) |
Subjects: | Science > Mathematics > Probabilities. Mathematical statistics |
Department: | Faculty of Science > Mathematics and Statistics |
Depositing user: | Pure Administrator |
Date deposited: | 22 Dec 2014 11:03 |
Last modified: | 04 Feb 2021 03:52 |
URI: | https://strathprints.strath.ac.uk/id/eprint/50863 |
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