Primal Discontinuous Galerkin Methods for Time-Dependent Coupled Surface and Subsurface Flow

Authors:
Ayçıl Çeşmelioğlu;Béatrice Rivière
Affiliations:
Department of Computational and Applied Mathematics, Rice University, Houston, USA 77005;Department of Computational and Applied Mathematics, Rice University, Houston, USA 77005
Venue:
Journal of Scientific Computing
Year:
2009

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Foreword

Journal of Scientific Computing

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Abstract

This paper introduces and analyzes a numerical method based on discontinuous finite element methods for solving the two-dimensional coupled problem of time-dependent incompressible Navier-Stokes equations with the Darcy equations through Beaver-Joseph-Saffman's condition on the interface. The proposed method employs Crank-Nicolson discretization in time (which requires one step of a first order scheme namely backward Euler) and primal DG method in space. With the correct assumption on the first time step optimal error estimates are obtained that are high order in space and second order in time.