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

Dietmar Kröner and Mirko Rokyta

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.

MSC 2010: 65N15; 35J25; 76M25

Acknowledgement

The authors want to thank the unknown referees for their valuable comments.

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

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Received: 2016-6-13
Revised: 2016-11-7
Accepted: 2017-1-19
Published Online: 2017-1-29
Published in Print: 2018-3-26

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