Geodesic
Error estimates for barycentric finite volumes combined with nonconforming finite elements applied to nonlinear convection-diffusion problems
Applications of Mathematics, Tome 47 (2002) no. 4, pp. 301-340 Cet article a éte moissonné depuis la source Czech Digital Mathematics Library

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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.
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.
DOI : 10.1023/A:1021701705932
Classification : 35K57, 35K60, 65M12, 65M15, 65M50, 65M60, 76M10, 76M12, 76M25, 76R99
Keywords: nonlinear convection-diffusion problem; compressible Navier-Stokes equations; cascade flow; barycentric finite volumes; Crouzeix-Raviart nonconforming piecewise linear finite elements; monotone finite volume scheme; discrete maximum principle; a priori estimates; error estimates 
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     author = {Dolej\v{s}{\'\i}, V{\'\i}t and Feistauer, Miloslav and Felcman, Ji\v{r}{\'\i} and Klikov\'a, Alice},
     title = {Error estimates for barycentric finite volumes combined with nonconforming finite elements applied to nonlinear convection-diffusion problems},
     journal = {Applications of Mathematics},
     pages = {301--340},
     year = {2002},
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     zbl = {1090.76550},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.1023/A:1021701705932/}
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Dolejší, Vít; Feistauer, Miloslav; Felcman, Jiří; Kliková, Alice. Error estimates for barycentric finite volumes combined with nonconforming finite elements applied to nonlinear convection-diffusion problems. Applications of Mathematics, Tome 47 (2002) no. 4, pp. 301-340. doi: 10.1023/A:1021701705932

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