deal.II Implementation of a Weak Galerkin Finite Element Solver for Darcy Flow

  • Zhuoran Wang
  • Graham Harper
  • Patrick O’Leary
  • Jiangguo LiuEmail author
  • Simon Tavener
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 11539)


This paper presents a weak Galerkin (WG) finite element solver for Darcy flow and its implementation on the deal.II platform. The solver works for quadrilateral and hexahedral meshes in a unified way. It approximates pressure by Q-type degree \(k({\ge }0)\) polynomials separately defined in element interiors and on edges/faces. Numerical velocity is obtained in the unmapped Raviart-Thomas space \( RT_{[k]} \) via postprocessing based on the novel concepts of discrete weak gradients. The solver is locally mass-conservative and produces continuous normal fluxes. The implementation in deal.II allows polynomial degrees up to 5. Numerical experiments show that our new WG solver performs better than the classical mixed finite element methods.


Darcy flow deal.II Finite element methods Hexahedral meshes Quadrilateral meshes Weak Galerkin 


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Copyright information

© Springer Nature Switzerland AG 2019

Authors and Affiliations

  • Zhuoran Wang
    • 1
  • Graham Harper
    • 1
  • Patrick O’Leary
    • 2
  • Jiangguo Liu
    • 1
    Email author
  • Simon Tavener
    • 1
  1. 1.Colorado State UniversityFort CollinsUSA
  2. 2.Kitware, Inc.Santa FeUSA

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