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adaptive finite element method; elliptic partial differential equations; perturbation argument; boundary value problem; eigenvalue problem; convergence; nonlinear boundary value problem; nonlinear eigenvalue problem
We review some numerical analysis of an adaptive finite element method (AFEM) for a class of elliptic partial differential equations based on a perturbation argument. This argument makes use of the relationship between the general problem and a model problem, whose adaptive finite element analysis is existing, from which we get the convergence and the complexity of adaptive finite element methods for a nonsymmetric boundary value problem, an eigenvalue problem, a nonlinear boundary value problem as well as a nonlinear eigenvalue problem.
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