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Development of a P 2 element with optimal L 2 convergence for biharmonic equation
Author(s) -
Mu Lin,
Ye Xiu,
Zhang Shangyou
Publication year - 2019
Publication title -
numerical methods for partial differential equations
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.901
H-Index - 61
eISSN - 1098-2426
pISSN - 0749-159X
DOI - 10.1002/num.22361
Subject(s) - biharmonic equation , mathematics , polygon mesh , finite element method , rectangle , rate of convergence , norm (philosophy) , discontinuous galerkin method , convergence (economics) , galerkin method , mathematical analysis , geometry , boundary value problem , physics , computer science , computer network , channel (broadcasting) , political science , law , economics , thermodynamics , economic growth
It is well known that convergence rate of finite element approximation is suboptimal in the L 2 norm for solving biharmonic equations when P 2 or Q 2 element is used. The goal of this paper is to derive a weak Galerkin (WG) P 2 element with the L 2 optimal 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.