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

Abstract

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.

Authors:
 [1];  [1];  [2];  [1];  [1]
  1. Colorado State Univ., Fort Collins, CO (United States)
  2. Kitware, Inc., Clifton Park, NY (United States)
Publication Date:
Research Org.:
Kitware, Inc., Clifton Park, NY (United States)
Sponsoring Org.:
USDOE Office of Science (SC), Advanced Scientific Computing Research (ASCR) (SC-21); USDOE Office of Science (SC), Basic Energy Sciences (BES) (SC-22). Chemical Sciences, Geosciences & Biosciences Division; National Science Foundation (NSF)
OSTI Identifier:
1594093
Grant/Contract Number:  
SC0019609; DMS-1819252
Resource Type:
Accepted Manuscript
Journal Name:
Computational Science – ICCS 2019
Additional Journal Information:
Conference: International Conference on Computational Science, June 2019
Country of Publication:
United States
Language:
English
Subject:
54 ENVIRONMENTAL SCIENCES; Darcy flow; deal.II; Finite element methods; Hexahedral meshes; Quadrilateral meshes; and Weak Galerkin

Citation Formats

Wang, Zhuoran, Harper, Graham, O’Leary, Patrick, Liu, Jiangguo, and Tavener, Simon. deal.II Implementation of a Weak Galerkin Finite Element Solver for Darcy Flow. United States: N. p., 2019. Web. doi:10.1007/978-3-030-22747-0_37.
Wang, Zhuoran, Harper, Graham, O’Leary, Patrick, Liu, Jiangguo, & Tavener, Simon. deal.II Implementation of a Weak Galerkin Finite Element Solver for Darcy Flow. United States. doi:10.1007/978-3-030-22747-0_37.
Wang, Zhuoran, Harper, Graham, O’Leary, Patrick, Liu, Jiangguo, and Tavener, Simon. Sat . "deal.II Implementation of a Weak Galerkin Finite Element Solver for Darcy Flow". United States. doi:10.1007/978-3-030-22747-0_37.
@article{osti_1594093,
title = {deal.II Implementation of a Weak Galerkin Finite Element Solver for Darcy Flow},
author = {Wang, Zhuoran and Harper, Graham and O’Leary, Patrick and Liu, Jiangguo and Tavener, Simon},
abstractNote = {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.},
doi = {10.1007/978-3-030-22747-0_37},
journal = {Computational Science – ICCS 2019},
number = ,
volume = ,
place = {United States},
year = {2019},
month = {6}
}

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