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A priori error estimates for finite element discretization of semilinear elliptic equations with non-Lipschitz nonlinearities
In this paper we develop numerical analysis for finite element discretization of semilinear elliptic equations with potentially non-Lipschitz nonlinearites. The nonlinearity is essecially assumed to be continuous and monotonically decreasing including the case of non-Lipschitz or even non-H\"older continuous nonlinearities. For a direct discretization (without any regularization) with linear finite …