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Space-time discontinuous Galerkin method for the solution of fluid-structure interaction

Martin Balazovjech;  Miloslav Feistauer;  Jaromír Horáček;  Martin Hadrava;  Adam Kosík — 2018

Applications of Mathematics

The paper is concerned with the application of the space-time discontinuous Galerkin method (STDGM) to the numerical solution of the interaction of a compressible flow and an elastic structure. The flow is described by the system of compressible Navier-Stokes equations written in the conservative form. They are coupled with the dynamic elasticity system of equations describing the deformation of the elastic body, induced by the aerodynamical force on the interface between the gas and the elastic...

Stability analysis of the space-time discontinuous Galerkin method for nonstationary nonlinear convection-diffusion problems

Balázsová, Monika;  Feistauer, Miloslav;  Hadrava, Martin;  Kosík, Adam — 2015

Programs and Algorithms of Numerical Mathematics

This paper is concerned with the stability analysis of the space-time discontinuous Galerkin method for the solution of nonstationary, nonlinear, convection-diffusion problems. In the formulation of the numerical scheme we use the nonsymmetric, symmetric and incomplete versions of the discretization of diffusion terms and interior and boundary penalty. Then error estimates are briefly characterized. The main attention is paid to the investigation of unconditional stability of the method. Theoretical...

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