2024 Volume 14 Issue 3
Article Contents

Iury Igreja. STABILIZED PRIMAL AND DUAL HYBRID MIXED DGFEM FOR DARCY FLOW[J]. Journal of Applied Analysis & Computation, 2024, 14(3): 1269-1301. doi: 10.11948/20230087
Citation: Iury Igreja. STABILIZED PRIMAL AND DUAL HYBRID MIXED DGFEM FOR DARCY FLOW[J]. Journal of Applied Analysis & Computation, 2024, 14(3): 1269-1301. doi: 10.11948/20230087

STABILIZED PRIMAL AND DUAL HYBRID MIXED DGFEM FOR DARCY FLOW

  • Corresponding author: Email: iuryigreja@ice.ufjf.br(I. Igreja)
  • Fund Project: This study is supported by CAPES (Brazil grant 88881.708850/2022-01), CNPq (Brazil grants 405366/2021-3 and 305353/2022-5) and FAPEMIG (Brazil grant APQ-00517-21)
  • This work presents and analyzes two stabilized mixed hybrid Discontinuous Galerkin Finite Element Methods (DGFEM) for Darcy flows. The difference between the methodologies lies in the choice of Lagrange multipliers that aim to weakly enforce continuity on the edge/face of the elements. Thus, we study methods with multipliers associated with the normal component of the velocity field and the trace of the pressure field that naturally gives rise, respectively, to primal and dual formulations. However, despite the difference between the formulations, both methods can be associated with the same discontinuous Galerkin formulation. In this sense, the analysis of consistency, existence, uniqueness, and error estimates is similar for both methods, even when continuous interpolations are employed to approximate the Lagrange multipliers. Moreover, stability and convergence rate are improved by adding the least-squares residual forms of the governing equations. Besides, for specific edge/face stabilization parameter choices, the methods become locally conservative, allowing the use of non-conforming Raviart-Thomas spaces. Finally, to illustrate the accuracy, convergence rates, local mass conservation, computational efficiency, and flexibility of the methods, several two and three-dimensional numerical experiments are performed considering homogeneous and heterogeneous porous media.

    MSC: 65N12, 65N15, 65N30, 76S05
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