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We develop a new technique for a posteriori error estimates suitable to parabolic and hyperbolic equations solved by the method of lines. This approach is applied to a general nonlinear parabolic problem with a strongly monotone elliptic operator , to a linear nonstationary convection-diiusion problem and a linear second order hyperbolic problem. The error… (More)

The paper deals with numerical simulation of a compressible flow in time-dependent 2D domains with a special interest in medical applications to airflow in the human vocal tract. The mathematical model of this process is described by the compressible Navier-Stokes equations. For the treatment of the time-dependent domain, the arbitrary Lagrangian-Eulerian… (More)

This work is concerned with the simulation of inviscid compressible flow in time dependent domains. We present an ALE (Arbitrary Lagrangian-Eulerian) formulation of the Euler equations describing compressible flow, discretize them in space by the discontinous Galerkin method and introduce a semi-implicit linearized time stepping for the numerical solution… (More)

- Miloslav Feistauer, Ji R Felcman, Gerald Warnecke
- 2007

The subject of the paper is the analysis of error estimates of the combined nite volume-nite element method for the numerical solution of a scalar nonlinear conservation law equation with a diiusion term. Nonlinear convective terms are approximated with the aid of a monotone nite volume scheme considered over the nite volume mesh dual to a triangular grid,… (More)

- M Feistauer, V Dolejší, V Kučera, V Sobotíková, Miloslav Feistauer, V Dolejš´i +2 others
- 2009

This paper is devoted to the analysis of the discontinuous Galerkin finite element method (DGFEM) applied to the space semidiscretization of a nonlinear nonstationary convection-diffusion Dirichlet problem. General nonconforming simplicial meshes are considered and the SIPG scheme is used. Under the assumption that the exact solution is sufficiently regular… (More)