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Journal of Numerical Mathematics

Editor-in-Chief: Hoppe, Ronald H. W. / Kuznetsov, Yuri

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Volume 26, Issue 1

Issues

Error estimates for higher-order finite volume schemes for convection–diffusion problems

Dietmar Kröner
  • Universität Freiburg, Institut für Angewandte Mathematik, Hermann-Herder-Str. 10, 79104, Freiburg, Germany
  • Other articles by this author:
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/ Mirko Rokyta
  • Corresponding author
  • Charles University, Department of Mathematical Analysis, Sokolovská 83, 186 75, Praha, Czech Republic
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Published Online: 2017-01-29 | DOI: https://doi.org/10.1515/jnma-2016-1056

Abstract

It is still an open problem to prove a priori error estimates for finite volume schemes of higher order MUSCL type, including limiters, on unstructured meshes, which show some improvement compared to first order schemes. In this paper we use these higher order schemes for the discretization of convection dominated elliptic problems in a convex bounded domain Ω in ℝ2 and we can prove such kind of an a priori error estimate. In the part of the estimate, which refers to the discretization of the convective term, we gain h1/2. Although the original problem is linear, the numerical problem becomes nonlinear, due to MUSCL type reconstruction/limiter technique.

Keywords: linear convection dominated diffusion equation in 2D; upwind finite volume scheme; first and higher order finite volume schemes; a priori error estimates; MUSCL type reconstruction/limiter

MSC 2010: 65N15; 35J25; 76M25

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About the article

Received: 2016-06-13

Revised: 2016-11-07

Accepted: 2017-01-19

Published Online: 2017-01-29

Published in Print: 2018-03-26


Funding: M. Rokyta was partially supported by Prvouk P47.


Citation Information: Journal of Numerical Mathematics, Volume 26, Issue 1, Pages 35–62, ISSN (Online) 1569-3953, ISSN (Print) 1570-2820, DOI: https://doi.org/10.1515/jnma-2016-1056.

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