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Nonconforming quadrilateral finite element method for nonlinear Kirchhoff‐type equation with damping
Author(s) -
Shi Dongyang,
Wu Yanmi
Publication year - 2019
Publication title -
mathematical methods in the applied sciences
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.719
H-Index - 65
eISSN - 1099-1476
pISSN - 0170-4214
DOI - 10.1002/mma.6065
Subject(s) - mathematics , quadrilateral , finite element method , mathematical analysis , nonlinear system , norm (philosophy) , type (biology) , partial differential equation , term (time) , physics , ecology , quantum mechanics , biology , political science , law , thermodynamics
Nonconforming quadrilateral E Q 1 r o tfinite element method (FEM) of nonlinear Kirchhoff‐type equation with damping is studied on anisotropic meshes. Based on the property of the nonlocal term of this equation, unconditional optimal error estimates of O ( h ) and O ( h + τ 2 ) ( h , the spatial parameter, and τ , the time step) in the brokenH 1norm are deduced for the semidiscrete and a linearized fully discrete schemes without any restrictions of τ through a distinct approach compared with the methods used for other partial differential equations, respectively. Besides, the damping term appearing in the Kirchhoff‐type equation is solved with a novel technique, which is the major difficulty in the theoretical analysis. Finally, some numerical results are provided to verify the theoretical analysis.