This work is concerned with the theoretical analysis of the space-time discontinuous Galerkin method applied to the numerical solution of nonstationary nonlinear convection-diffusion problem in a time- dependent domain. At first, the problem is reformulated by the use of the arbitrary Lagrangian-Eulerian (ALE) method, which replaces the classical partial time derivative by the so-called ALE derivative and an additional convection term. Then the problem is discretized with the use of the ALE space-time discontinuous Galerkin method. On the basis of a technical analysis we obtain an unconditional stability of this method. An important step in the analysis is the generalization of a discrete characteristic function associated with the approximate solutionin a time-dependentdomainand the derivationof its properties. Further we derive an a priori error estimate of the method in terms of the interpolation error, as well as in terms of h and tau. Finally, some practical applications of the ALE space-time discontinuos Galerkin method in a time-dependent domain are given. We are concerned with the numerical solution of a nonlinear elasticity benchmark problem and moreover with the interaction of compressible viscous flow with elastic structures. The main attention is paid to the modeling of flow induced vocal fold...
| Identifer | oai:union.ndltd.org:nusl.cz/oai:invenio.nusl.cz:445724 |
| Date | January 2021 |
| Creators | Balázsová, Monika |
| Contributors | Feistauer, Miloslav, Dumbser, Michael, Bause, Markus |
| Source Sets | Czech ETDs |
| Language | English |
| Detected Language | English |
| Type | info:eu-repo/semantics/doctoralThesis |
| Rights | info:eu-repo/semantics/restrictedAccess |
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