Analysis of \(hp\) discontinuous Galerkin methods for incompressible two-phase flow. (English) Zbl 1157.76024
Summary: We prove the convergence of a class of discontinuous Galerkin methods for solving the fully coupled incompressible two-phase flow problem in the non-degenerate case. Estimates in both the mesh size and the polynomial degrees are obtained. Numerical convergence rates confirm the theoretical results.
MSC:
| 76M10 | Finite element methods applied to problems in fluid mechanics |
| 76T10 | Liquid-gas two-phase flows, bubbly flows |
| 76S05 | Flows in porous media; filtration; seepage |
| 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 |
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