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A stabilizer free weak Galerkin finite element method with supercloseness of order two
Author(s) -
AlTaweel Ahmed,
Wang Xiaoshen,
Ye Xiu,
Zhang Shangyou
Publication year - 2021
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.22564
Subject(s) - mathematics , finite element method , galerkin method , discontinuous galerkin method , mixed finite element method , smoothed finite element method , extended finite element method , order (exchange) , mathematical analysis , hp fem , partial differential equation , finite element limit analysis , stabilizer (aeronautics) , element (criminal law) , boundary knot method , boundary element method , physics , structural engineering , finance , engineering , economics , thermodynamics , political science , law
The weak Galerkin (WG) finite element method is an effective and flexible general numerical technique for solving partial differential equations. A simple WG finite element method is introduced for second‐order elliptic problems. First we have proved that stabilizers are no longer needed for this WG element. Then we have proved the supercloseness of order two for the WG finite element solution. The numerical results confirm the theory.