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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 presents the theory of the space-time discontinuous Galerkin finite element method for the discretization of a nonstationary convection-diffusion initial-boundary value problem with nonlinear convection and nonlinear diffusion. The discon-tinuous Galerkin method is applied separately in space and time using, in general, different space grids on(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)
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)
The paper presents main results of the investigation of the coupled BEM and FEM applied to a nonlinear generally nonmonotone exterior boundary value problem. The problem consists of a nonlinear diier-ential equation considered in an annular bounded domain and the Laplace equation outside. These equations are equipped with boundary and transmission(More)