The numerical analysis of DG method for convection-diffusion problem

0380005 - ÚT 2013 DE eng A - Abstrakt
Kosík, Adam - Feistauer, M. - Hadrava, M.
The numerical analysis of DG method for convection-diffusion problem.
Modeling and Simulation of Transport Phenomena - book of abstracts. Erlangen: University Erlangen-Nuremberg, 2012 - (Kuzmin, D.). s. 20-20
[Modeling and Simulation of Transport Phenomena. 30.07.2012-01.08.2012, Moselle Valley]
Grant CEP: GA ČR(CZ) GAP101/11/0207
Výzkumný záměr: CEZ:AV0Z20760514
Klíčová slova: discontinuous Galerkin method * Navier-Stokes equation * fluid-structure interaction
Kód oboru RIV: BI - Akustika a kmity

The discontinuous Galerkin method (DMG) has become popular for solving complicated problems. Our motivation is to analyse the method numerically on the some simple cases. The scalar nonstationary nonlinear convection-diffusion equation is considered. Two different approaches for the time-discretization are compared. We apply a backward-difference formula and the full space-time discontinuous Galerkin scheme. A robust implementation of the DGM discretization was worked out with the aid of NET library. The solver allows the user choose an arbitrary degree of polynomial approximation both in time and space, provided a sufficiently accurate quadrature rule is given. For the solution of the resulting system of linear algebraic equations the direct solver UMFPACK was used. The computations on some test cases were performed and obtained numerical results are presented.
Trvalý link: http://hdl.handle.net/11104/0210836