# Discontinuous Galerkin Method For The Fluid-structure Interaction

## Main Article Content

## Abstract

The subject of the paper is the brief description of the stability analysis of the space-time discontinuous Galerkin method for the numerical solution of a model nonlinear parabolic problem in a time dependent domain. The analyzed method is used for the solution of compressible flow in a time-dependent domain and interacted with an elastic body, applied to the simulation of vocal fold flow-induced vibrations.

## Article Details

How to Cite

Feistauer, M., Balázsová, M., & Horáček, J.
(2020).
Discontinuous Galerkin Method For The Fluid-structure Interaction.

*Proceedings Of The Conference Algoritmy,*, 61 - 70. Retrieved from http://www.iam.fmph.uniba.sk/amuc/ojs/index.php/algoritmy/article/view/1555/819
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Articles

## References

[1] M. Balázsová and M. Feistauer, On the uniform stability of the space-time discontinuous Galerkin method for nonstationary problems in time-dependent domains, ALGORITMY 2016, 20th Conference on Scientific Computing, Vysoké Tatry - Podbanské, Slovakia, March 13-18, 2016, Eds. Angela Handlovičová, Daniel Šečovič, Slovak University of Technology in Bratislava, Faculty of Civil Engineering, Department of Mathematics and Descriptive Geometry, pp. 84-92.

[2] M. Balázsová and M. Feistauer, On the stability of the ALE space-time discontinuous Galerkin method for nonlinear convection-diffusion problems in time-dependent domains, Applied Mathematics, 60 (2015), pp. 501-526.

[3] J. Česenek, M. Feistauer and A Kosı́k, DGFEM for the analysis of airfoil vibrations induced by compressible flow, Z. Angew. Math. Mech., 93 (2013), pp. 387-402.

[4] P. G. Ciarlet, Mathematical Elasticity, Volume I, Three-Dimensional Elasticity, Volume 20 of Studies in Mathematics and its Applications, Elsevier Science Publishers B.V., Amsterdam, 1988.

[5] V. Dolejšı́ and M. Feistauer, Discontinuous Galerkin Method, Analysis and Applications to Compressible Flow, Springer, Cham, 2015.

[2] M. Balázsová and M. Feistauer, On the stability of the ALE space-time discontinuous Galerkin method for nonlinear convection-diffusion problems in time-dependent domains, Applied Mathematics, 60 (2015), pp. 501-526.

[3] J. Česenek, M. Feistauer and A Kosı́k, DGFEM for the analysis of airfoil vibrations induced by compressible flow, Z. Angew. Math. Mech., 93 (2013), pp. 387-402.

[4] P. G. Ciarlet, Mathematical Elasticity, Volume I, Three-Dimensional Elasticity, Volume 20 of Studies in Mathematics and its Applications, Elsevier Science Publishers B.V., Amsterdam, 1988.

[5] V. Dolejšı́ and M. Feistauer, Discontinuous Galerkin Method, Analysis and Applications to Compressible Flow, Springer, Cham, 2015.