# Article

 Title: Analysis of the discontinuous Galerkin finite element method applied to a scalar nonlinear convection-diffusion equation (English) Author: Hozman, Jiří Author: Dolejší, Vít Language: English Journal: Programs and Algorithms of Numerical Mathematics Volume: Proceedings of Seminar. Dolní Maxov, June 1-6, 2008 Issue: 2008 Year: Pages: 97-102 . Category: math . Summary: We deal with a scalar nonstationary convection-diffusion equation with nonlinear convective as well as diffusive terms which represents a model problem for the solution of the system of the compressible Navier-Stokes equations describing a motion of viscous compressible fluids. We present a discretization of this model equation by the discontinuous Galerkin finite element method. Moreover, under some assumptions on the nonlinear terms, domain partitions and the regularity of the exact solution, we introduce a priori error estimates in the $L^\infty(0,T; L^2(\Omega))$-norm and in the $L^2(0,T; H^1(\Omega))$-seminorm. A sketch of the proof is presented. () MSC: 76-xx idZBL: Zbl 05802248 . Date available: 2015-09-08T11:34:43Z Last updated: 2015-12-04 Stable URL: http://hdl.handle.net/10338.dmlcz/702862 .

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