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Quasi‐uniform convergence analysis of a modified penalty finite element method for nonlinear singularly perturbed bi‐wave problem
Author(s) -
Wu Yanmi,
Shi Dongyang
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.22607
Subject(s) - mathematics , finite element method , bilinear interpolation , norm (philosophy) , penalty method , nonlinear system , term (time) , mixed finite element method , mathematical analysis , perturbation (astronomy) , interpolation (computer graphics) , finite element limit analysis , bilinear form , convergence (economics) , mathematical optimization , animation , statistics , physics , computer graphics (images) , quantum mechanics , political science , computer science , law , economics , thermodynamics , economic growth
In this paper, a modified penalty finite element method (FEM) for solving the nonlinear singularly perturbed bi‐wave problem with a rectangular Morley element is presented. The second order term, the nonlinear term, and the source term are approximated by the bilinear interpolation part (conforming part) instead of the whole function on each element, respectively. The well‐posedness of the approximation solution is proved through Brouwer fixed point theorem. Quasi‐uniform optimal error estimate in the energy norm is derived independent of the negative powers of the real perturbation parameter δ appearing in the considered problem, which improves the corresponding result in the existing literature. Finally, some numerical results are given to verify the theoretical analysis.