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

Conference · Sat Jun 08 00:00:00 EDT 2019

DOI:https://doi.org/10.1007/978-3-030-22747-0_37· OSTI ID:1594093

Wang, Zhuoran ^[1]; Harper, Graham ^[1]; O’Leary, Patrick ^[2]; Liu, Jiangguo ^[1]; Tavener, Simon ^[1]

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1. Colorado State Univ., Fort Collins, CO (United States)
2. Kitware, Inc., Clifton Park, NY (United States)

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 $k(≥ 0)$ polynomials separately defined in element interiors and on edges/faces. In this work, 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.

• Research Organization: Kitware, Inc., Clifton Park, NY (United States)
• Sponsoring Organization: USDOE Office of Science (SC), Advanced Scientific Computing Research (ASCR); USDOE Office of Science (SC), Basic Energy Sciences (BES). Chemical Sciences, Geosciences, and Biosciences Division; National Science Foundation (NSF)
• DOE Contract Number: SC0019609; DMS-1819252
• OSTI ID: 1594093
• Resource Relation: Conference: International Conference on Computational Science, Faro (Portugal), 12-14 Jun 2019; Related Information: From, proceedings, part IV
• Country of Publication: United States
• Language: English

Related Subjects

54 ENVIRONMENTAL SCIENCES
Darcy flow
deal.II
Finite element methods
Hexahedral meshes
Quadrilateral meshes
and Weak Galerkin