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Title: Development of a P 2 element with optimal L 2 convergence for biharmonic equation

It is well known that convergence rate of finite element approximation is suboptimal in theL2norm for solving biharmonic equations whenP2orQ2element is used. The goal of this paper is to derive a weak Galerkin (WG)P2element with theL2optimal convergence rate by assuming the exact solution sufficiently smooth. In addition, our new WG finite element method can be applied to general mesh such as hybrid mesh, polygonal mesh or mesh with hanging node. The numerical experiments have been conducted on different meshes including hybrid meshes with mixed of pentagon and rectangle and mixed of hexagon and triangle.

 
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NSF-PAR ID:
10461498
Author(s) / Creator(s):
 ;  ;  
Publisher / Repository:
Wiley Blackwell (John Wiley & Sons)
Date Published:
Journal Name:
Numerical Methods for Partial Differential Equations
Volume:
35
Issue:
4
ISSN:
0749-159X
Page Range / eLocation ID:
p. 1497-1508
Format(s):
Medium: X
Sponsoring Org:
National Science Foundation
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