Analysis of the discontinuous Galerkin method for nonlinear convection–diffusion problems

• Published in: Computer methods in applied mechanics and engineering Vol. 194; no. 25; pp. 2709 - 2733
• Main Authors: Dolejší, V., Feistauer, M., Sobotíková, V.
• Format: Journal Article
• Language: English
• Published: Amsterdam Elsevier B.V 01.07.2005; Elsevier
• Subjects: Asymptotic error estimates; Discontinuous Galerkin finite element method; Exact sciences and technology; Fluid dynamics; Fundamental areas of phenomenology (including applications); General theory; Interior and boundary penalty; Nonlinear convection–diffusion equation; Nonsymmetric stabilization of diffusive terms; Numerical experiments; Physics; Turbulence simulation and modeling; Turbulent flows, convection, and heat transfer; 65M15; Nonsymmetric stabilization of diffusive terms; Asymptotic error estimates; Discontinuous Galerkin finite element method; Interior and boundary penalty; 28; Nonlinear convection–diffusion equation; 65M60; Numerical experiments; 65M12; 20; 86; Discontinuity; Error estimation; Stabilization; Nonlinear convection-diffusion equation; Convection diffusion equation; Experimental study; Galerkin-Petrov method; Finite element method; Polyhedron; Modelling; Asymptotic approximation; Convexity; Non linear effect
• ISSN: 0045-7825; 1879-2138
• DOI: 10.1016/j.cma.2004.07.017

The subject-matter is the analysis of the discontinuous Galerkin finite element method applied to a nonlinear convection–diffusion problem. In the contrary to the standard FEM the requirement of the conforming properties is omitted. This allows us to consider general polyhedral elements with mutually disjoint interiors. We do not require their convexity, but assume only that they are star-shaped. We present an error analysis for the case of a nonsymmetric discretization of diffusion terms. Theoretical results are accompanied by numerical experiments.