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Stability analysis of the ALE-STDGM for linear convection-diffusion-reaction problems in time-dependent domains. (English) Zbl 1352.65288

Karasözen, Bülent (ed.) et al., Numerical mathematics and advanced applications – ENUMATH 2015. Selected papers based on the presentations at the European conference, Ankara, Turkey, September 14–18, 2015. Cham: Springer (ISBN 978-3-319-39927-0/hbk; 978-3-319-39929-4/ebook). Lecture Notes in Computational Science and Engineering 112, 215-223 (2016).
Summary: 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 \(p\geq 1\), 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.
For the entire collection see [Zbl 1358.65003].

MSC:

65M12 Stability and convergence of numerical methods for initial value and initial-boundary value problems involving PDEs
65M30 Numerical methods for ill-posed problems for initial value and initial-boundary value problems involving PDEs
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