A prox-based semi-smooth Newton method is proposed for finite-element discretizations of convex variational problems, with global well-posedness and local superlinear convergence established under suitable assumptions on energy densities.
Lindqvist,Notes on the stationary p-Laplace equation,SpringerBriefs Math., Cham: Springer; Bilbao: BCAM – Basque Center for Applied Mathematics, 2019
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A $\operatorname{prox}$-Based Semi-Smooth Newton Method for Convex Variational Problems
A prox-based semi-smooth Newton method is proposed for finite-element discretizations of convex variational problems, with global well-posedness and local superlinear convergence established under suitable assumptions on energy densities.