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Article

Vlasák, Miloslav
Stability of ALE discontinuous Galerkin method with Radau quadrature. (English). In: Chleboun, J., Kůs, P., Přikryl, P., Rozložník, M., Segeth, K., Šístek, J. and Vejchodský, T. (eds.): Programs and Algorithms of Numerical Mathematics. Proceedings of Seminar. Hejnice, June 24-29, 2018. Institute of Mathematics CAS, Prague, 2019. pp. 169-176
MSC: 65M60, 65M99 | DOI: 10.21136/panm.2018.18
Keywords:
ALE formulation; discontinuous Galerkin method; implicit Runge-Kutta method; discrete characteristic function; stability
Summary:
We assume the nonlinear parabolic problem in a time dependent domain, where the evolution of the domain is described by a regular given mapping. The problem is discretized by the discontinuous Galerkin (DG) method modified by the right Radau quadrature in time with the aid of Arbitrary Lagrangian-Eulerian(ALE) formulation. The sketch of the proof of the stability of the method is shown.
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