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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. (English) Zbl 1090.76550

Appl. Math., Praha 47, No. 4, 301-340 (2002).
Summary: 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.

Cited in 9 Documents

MSC:

76M12 Finite volume methods applied to problems in fluid mechanics
76M25 Other numerical methods (fluid mechanics) (MSC2010)
65M12 Stability and convergence of numerical methods for initial value and initial-boundary value problems involving PDEs
65M50 Mesh generation, refinement, and adaptive methods for the numerical solution of initial value and initial-boundary value problems involving PDEs
35K60 Nonlinear initial, boundary and initial-boundary value problems for linear parabolic equations

Keywords:

nonlinear convection-diffusion problem; compressible Navier-Stokes equations; cascade flow; barycentric finite volumes; discrete maximum principle; a priori estimates; error estimates
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\textit{V. Dolejší} et al., Appl. Math., Praha 47, No. 4, 301--340 (2002; Zbl 1090.76550)
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References:

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