Abstract
In this paper we investigate the stability of the space-time discontinuous Galerkin method (STDGM) for the solution of nonstationary, linear convection-diffusion-reaction problem in time-dependent domains formulated with the aid of the arbitrary Lagrangian-Eulerian (ALE) method. At first we define the continuous problem and reformulate it using the ALE method, which replaces the classical partial time derivative with the so called ALE-derivative and an additional convective term. In the second part of the paper we discretize our problem using the space-time discontinuous Galerkin method. The space discretization uses piecewise polynomial approximations of degree p ≥ 1, in time we use only piecewise linear discretization. Finally in the third part of the paper we present our results concerning the unconditional stability of the method.
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References
M. Balázsová, M. Feistauer, M. Hadrava, A. Kosík, On the stability of the space-time discontinuous Galerkin method for the numerical solution of nonstationary nonlinear convection-diffusion problems. J. Numer. Math. 23 (3), 211–233 (2015)
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Acknowledgements
This research was supported by the grant 13-00522S of the Czech Science Foundation (M. Feistauer) and by the project GA UK No. 127615 of the Charles University in Prague (M. Balázsová).
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Balázsová, M., Feistauer, M. (2016). Stability Analysis of the ALE-STDGM for Linear Convection-Diffusion-Reaction Problems in Time-Dependent Domains. In: Karasözen, B., Manguoğlu, M., Tezer-Sezgin, M., Göktepe, S., Uğur, Ö. (eds) Numerical Mathematics and Advanced Applications ENUMATH 2015. Lecture Notes in Computational Science and Engineering, vol 112. Springer, Cham. https://doi.org/10.1007/978-3-319-39929-4_22
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DOI: https://doi.org/10.1007/978-3-319-39929-4_22
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