Abstract
We apply the class of Chen-Mangasarian smooth approximation functions and the smoothing Newton method proposed in [6] to solve a class of quasi-linear nonsmooth Dirichlet problems. We show that the smoothing Newton method converges globally and superlinearly for solving the system of nonsmooth equations arising from nonsmooth Dirichlet problems. Moreover, we show that the error bound for finite difference solution of smooth Poisson-type equations in a bounded domain [15] remains the same order for a class of nonsmooth equations. It is thus expected that the smoothing Newton method works well for nonsmooth Dirichlet problems. We report encouraging numerical results for three examples arising from a model of the ideal MHD equilibria.Key Wordsnonsmooth Dirichlet problemerror boundsmoothing Newton methods.
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