Communications on Applied Mathematics and Computation >

2022 , Vol. 4 >Issue 1: 293 - 318

DOI: https://doi.org/10.1007/s42967-020-00115-0

A Compatible Embedded-Hybridized Discontinuous Galerkin Method for the Stokes-Darcy-Transport Problem

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  • 1 Department of Mathematics and Statistics, Oakland University, Rochester, MI 48309, USA;
    2 Department of Applied Mathematics, University of Waterloo, Waterloo, ON N2L 3G1, Canada

Received date: 2020-04-27

  Revised date: 2020-11-18

  Online published: 2022-03-01

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Abstract

We present a stability and error analysis of an embedded-hybridized discontinuous Galerkin (EDG-HDG) finite element method for coupled Stokes-Darcy flow and transport. The flow problem, governed by the Stokes-Darcy equations, is discretized by a recently introduced exactly mass conserving EDG-HDG method while an embedded discontinuous Galerkin (EDG) method is used to discretize the transport equation. We show that the coupled flow and transport discretization are compatible and stable. Furthermore, we show the existence and uniqueness of the semi-discrete transport problem and develop optimal a priori error estimates. We provide numerical examples illustrating the theoretical results. In particular, we compare the compatible EDG-HDG discretization to a discretization of the coupled Stokes-Darcy and transport problem that is not compatible. We demonstrate that where the incompatible discretization may result in spurious oscillations in the solution to the transport problem, the compatible discretization is free of oscillations. An additional numerical example with realistic parameters is also presented.

Key words： Stokes-Darcy flow; Coupled flow and transport; Beavers-Joseph-Saffman; Embedded and hybridized methods; Discontinuous Galerkin; Multiphysics

Cite this article

Aycil Cesmelioglu, Sander Rhebergen . A Compatible Embedded-Hybridized Discontinuous Galerkin Method for the Stokes-Darcy-Transport Problem[J]. Communications on Applied Mathematics and Computation, 2022 , 4(1) : 293 -318 . DOI: 10.1007/s42967-020-00115-0

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