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Time-discrete higher-order ALE formulations: stability. (English) Zbl 1267.65114
This paper is concerned with time-discrete discontinuous Galerkin numerical schemes of any order for a time-dependent advection-diffusion model in moving domains. A particular emphasis is put on the stability property of the numerical scheme which relies on the validity of the Reynolds’ identity for the discontinuous Galerkin method. The approach in the paper extends the geometric conservation law to higher-order methods. Numerical experiments support the theoretical findings.

MSC:
65M12 Stability and convergence of numerical methods for initial value and initial-boundary value problems involving PDEs
65M60 Finite element, Rayleigh-Ritz and Galerkin methods for initial value and initial-boundary value problems involving PDEs
35K20 Initial-boundary value problems for second-order parabolic equations
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