Analysis of hp discontinuous Galerkin methods for incompressible two-phase flow

Authors:
Yekaterina Epshteyn;Beatrice Rivière
Affiliations:
Department of Mathematical Sciences and Center for Nonlinear Analysis, Carnegie Mellon University, Pittsburgh, PA 15213, USA;Department of Computational and Applied Mathematics, Rice University, 6100 Main Street, Houston, TX 77005, USA
Venue:
Journal of Computational and Applied Mathematics
Year:
2009

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Abstract

In this paper, 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.