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Title: Effective implementation of the weak Galerkin finite element methods for the biharmonic equation

Abstract

The weak Galerkin (WG) methods have been introduced in [11, 12, 17] for solving the biharmonic equation. The purpose of this paper is to develop an algorithm to implement the WG methods effectively. This can be achieved by eliminating local unknowns to obtain a global system with significant reduction of size. In fact this reduced global system is equivalent to the Schur complements of the WG methods. The unknowns of the Schur complement of the WG method are those defined on the element boundaries. The equivalence of theWG method and its Schur complement is established. The numerical results demonstrate the effectiveness of this new implementation technique.

Authors:
ORCiD logo [1];  [2];  [3]
  1. Oak Ridge National Lab. (ORNL), Oak Ridge, TN (United States)
  2. National Science Foundation (NSF), Arlington, VA (United States)
  3. Univ. of Arkansas, Little Rock, AR (United States)
Publication Date:
Research Org.:
Oak Ridge National Lab. (ORNL), Oak Ridge, TN (United States)
Sponsoring Org.:
USDOE
OSTI Identifier:
1394427
Grant/Contract Number:
AC05-00OR22725
Resource Type:
Journal Article: Accepted Manuscript
Journal Name:
Computers and Mathematics with Applications (Oxford)
Additional Journal Information:
Journal Name: Computers and Mathematics with Applications (Oxford); Journal Volume: 74; Journal Issue: 6; Journal ID: ISSN 0898-1221
Publisher:
Elsevier
Country of Publication:
United States
Language:
English
Subject:
97 MATHEMATICS AND COMPUTING

Citation Formats

Mu, Lin, Wang, Junping, and Ye, Xiu. Effective implementation of the weak Galerkin finite element methods for the biharmonic equation. United States: N. p., 2017. Web. doi:10.1016/j.camwa.2017.06.002.
Mu, Lin, Wang, Junping, & Ye, Xiu. Effective implementation of the weak Galerkin finite element methods for the biharmonic equation. United States. doi:10.1016/j.camwa.2017.06.002.
Mu, Lin, Wang, Junping, and Ye, Xiu. Thu . "Effective implementation of the weak Galerkin finite element methods for the biharmonic equation". United States. doi:10.1016/j.camwa.2017.06.002.
@article{osti_1394427,
title = {Effective implementation of the weak Galerkin finite element methods for the biharmonic equation},
author = {Mu, Lin and Wang, Junping and Ye, Xiu},
abstractNote = {The weak Galerkin (WG) methods have been introduced in [11, 12, 17] for solving the biharmonic equation. The purpose of this paper is to develop an algorithm to implement the WG methods effectively. This can be achieved by eliminating local unknowns to obtain a global system with significant reduction of size. In fact this reduced global system is equivalent to the Schur complements of the WG methods. The unknowns of the Schur complement of the WG method are those defined on the element boundaries. The equivalence of theWG method and its Schur complement is established. The numerical results demonstrate the effectiveness of this new implementation technique.},
doi = {10.1016/j.camwa.2017.06.002},
journal = {Computers and Mathematics with Applications (Oxford)},
number = 6,
volume = 74,
place = {United States},
year = {Thu Jul 06 00:00:00 EDT 2017},
month = {Thu Jul 06 00:00:00 EDT 2017}
}

Journal Article:
Free Publicly Available Full Text
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