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Error Estimates for Barycentric Finite Volumes Combined with Nonconforming Finite Elements Applied to Nonlinear Convection-Diffusion Problems

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Abstract

The subject of the paper is the derivation of error estimates for the combined finite volume-finite element method used for the numerical solution of nonstationary nonlinear convection-diffusion problems. Here we analyze the combination of barycentric finite volumes associated with sides of triangulation with the piecewise linear nonconforming Crouzeix-Raviart finite elements. Under some assumptions on the regularity of the exact solution, the L 2(L 2) and L 2(H 1) error estimates are established. At the end of the paper, some computational results are presented demonstrating the application of the method to the solution of viscous gas flow.

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Authors and Affiliations

  1. Institute of Numerical Mathematics, Faculty of Mathematics and Physics, Charles University, Sokolovska 83, 186 75, Praha 8, Czech Republic

    Vit Dolejsi, Miloslav Feistauer & Jiri Felcman

  2. Centre for Theoretical Study, Charles University, Jilska 1, 110 00, Praha 1, Czech Republic

    Alice Klikova

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  1. Vit Dolejsi
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  2. Miloslav Feistauer
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  3. Jiri Felcman
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  4. Alice Klikova
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Dolejsi, V., Feistauer, M., Felcman, J. et al. Error Estimates for Barycentric Finite Volumes Combined with Nonconforming Finite Elements Applied to Nonlinear Convection-Diffusion Problems. Applications of Mathematics 47, 301–340 (2002). https://doi.org/10.1023/A:1021701705932

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