A  C  0 ‐weak  G alerkin finite element method for fourth‐order elliptic problems | Zendy

Chen Gang | Zendy; Feng Minfu | Zendy

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A C 0 ‐weak G alerkin finite element method for fourth‐order elliptic problems

Author(s) -

Chen Gang,

Feng Minfu

Publication year - 2016

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.22050

Subject(s) - biharmonic equation , piecewise , mathematics , galerkin method , finite element method , discontinuous galerkin method , degree of a polynomial , polynomial , degree (music) , partial differential equation , order (exchange) , mathematical analysis , boundary value problem , physics , finance , economics , thermodynamics , acoustics

This article proposes and analyzes a C 0 ‐weak Galerkin (WG) finite element method for solving the biharmonic equation in two‐dimensional and three‐dimensional. The new WG method uses continuous piecewise‐polynomial approximations of degree k + 2 ( k ≥ 0 ) for the unknown u and discontinuous piecewise‐polynomial approximations of degree k for the trace of ∇ u on the interelement boundaries. Optimal error estimates are obtained in H 2 , H 1 , and L 2 norms. Numerical experiments illustrate and confirm the theoretical results. © 2016 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq 32: 1090–1104, 2016

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