NDLI: Lowest-Order Weak Galerkin Finite Element Method for Darcy Flow on Convex Polygonal Meshes

Content Provider	Society for Industrial and Applied Mathematics (SIAM)
Author	Liu, Jiangguo Tavener, Simon Wang, Zhuoran
Copyright Year	2018
Abstract	This paper presents the lowest-order weak Galerkin (WG) finite element method for solving the Darcy equation or elliptic boundary value problems on general convex polygonal meshes. In this approach, constants are used in element interiors and on edges to approximate the primal variable (pressure). The discrete weak gradients of these constant basis functions are established in simple $H(div)$-subspaces on polygons that are explicitly constructed by using the normalized coordinates and Wachspress coordinates [W. Chen and Y. Wang, Math. Comp., 86 (2017), pp. 2053--2087]. These discrete weak gradients are used to approximate the classical gradient in the variational formulation. No penalization is needed for this new method. The method results in symmetric positive-definite sparse linear systems. It is locally mass-conservative and produces continuous normal fluxes. The new method has optimal-order convergence in pressure, velocity, and normal flux, when the convex polygon meshes are shape-regular.
Sponsorship	National Science Foundation
Starting Page	B1229
Ending Page	B1252
Page Count	24
File Format	PDF
ISSN	10648275
DOI	10.1137/17M1145677
e-ISSN	10957197
Issue Number	5
Volume Number	40
Language	English
Publisher	Society for Industrial and Applied Mathematics
Publisher Date	2018-09-13
Access Restriction	Subscribed
Subject Keyword	elliptic boundary value problems Wachspress coordinates lowest-order finite element methods polygonal meshes Error bounds Finite elements, Rayleigh-Ritz and Galerkin methods, finite methods Flows in porous media; filtration; seepage Darcy flow weak Galerkin
Content Type	Text
Resource Type	Article
Subject	Applied Mathematics Computational Mathematics

Sl.	Authority	Responsibilities	Communication Details
1	Ministry of Education (GoI), Department of Higher Education	Sanctioning Authority	https://www.education.gov.in/ict-initiatives
2	Indian Institute of Technology Kharagpur	Host Institute of the Project: The host institute of the project is responsible for providing infrastructure support and hosting the project	https://www.iitkgp.ac.in
3	National Digital Library of India Office, Indian Institute of Technology Kharagpur	The administrative and infrastructural headquarters of the project	Dr. B. Sutradhar bsutra@ndl.gov.in
4	Project PI / Joint PI	Principal Investigator and Joint Principal Investigators of the project	Dr. B. Sutradhar bsutra@ndl.gov.in Prof. Saswat Chakrabarti will be added soon
5	Website/Portal (Helpdesk)	Queries regarding NDLI and its services	support@ndl.gov.in
6	Contents and Copyright Issues	Queries related to content curation and copyright issues	content@ndl.gov.in
7	National Digital Library of India Club (NDLI Club)	Queries related to NDLI Club formation, support, user awareness program, seminar/symposium, collaboration, social media, promotion, and outreach	clubsupport@ndl.gov.in
8	Digital Preservation Centre (DPC)	Assistance with digitizing and archiving copyright-free printed books	dpc@ndl.gov.in
9	IDR Setup or Support	Queries related to establishment and support of Institutional Digital Repository (IDR) and IDR workshops	idr@ndl.gov.in