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math.NA2025
Newton's method in adaptive iteratively linearized FEM
Philipp Bringmann, Maximilian Brunner, Dirk Praetorius
This paper concerns the inclusion of Newton's method into an adaptive finite element method (FEM) for the solution of nonlinear partial differential equations (PDEs). It features a…
math.NA2025
Global convergence of adaptive least-squares finite element methods for nonlinear PDEs
Philipp Bringmann, Dirk Praetorius
The Zarantonello fixed-point iteration is an established linearization scheme for quasilinear PDEs with strongly monotone and Lipschitz continuous nonlinearity in Hilbert spaces. T…