Article
MSC:
35K57,
35K60,
65M12,
65M15,
65M50,
65M60,
76M10,
76M12,
76M25,
76R99 | MR 1914117 | Zbl 1090.76550 | DOI: 10.1023/A:1021701705932
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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
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
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.
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