Vit Dolejsi, Miloslav Feistauer, Jiri Felcman, Institute of Numerical Mathematics, Faculty of Mathematics and Physics, Charles University, Sokolovska 83, 186 75 Praha 8, Czech Republic, e-mail: dolejsi@karlin.mff.cuni.cz, feist@karlin.mff.cuni.cz, felcman@karlin.mff.cuni.cz; Alice Klikova, Centre for Theoretical Study, Charles University, Jilska 1, 110 00 Praha 1, Czech Republic, e-mail: klikova@cts.cuni.cz
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.
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
Classification (MSC 2000): 65M12, 65M50, 35K60, 76M10, 76M25
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