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

Dietmar Kröner 1  and Mirko Rokyta 2
  • 1 Universität Freiburg, Hermann-Herder-Str. 10, 79104, Freiburg, Germany
  • 2 Charles University, Sokolovská 83, 186 75, Praha, Czech Republic
Dietmar Kröner
  • Universität Freiburg, Institut für Angewandte Mathematik, Hermann-Herder-Str. 10, 79104, Freiburg, Germany
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and Mirko Rokyta
  • Corresponding author
  • Charles University, Department of Mathematical Analysis, Sokolovská 83, 186 75, Praha, Czech Republic
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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.

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