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20142024
most citedAn Adaptive Newton-Method Based on a Dynamical Systems Approach

40 citations · 51 across the 6 of their papers we have counts for

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Showing 2016Show all

3 papers · 1 filter

math.NA2016

Adaptive Pseudo-Transient-Continuation-Galerkin Methods for Semilinear Elliptic Partial Differential Equations

Mario Amrein, Thomas P. Wihler

In this paper we investigate the application of pseudo-transient-continuation (PTC) schemes for the numerical solution of semilinear elliptic partial differential equations, with p…

math.NA2016★ 40 cited

An Adaptive Newton-Method Based on a Dynamical Systems Approach

Mario Amrein, Thomas P. Wihler

The traditional Newton method for solving nonlinear operator equations in Banach spaces is discussed within the context of the continuous Newton method. This setting makes it possi…

math.NA2016★ 8 cited

An -Adaptive Newton-Galerkin Finite Element Procedure for Semilinear Boundary Value Problems

Mario Amrein, Jens M. Melenk, Thomas P. Wihler

In this paper we develop an -adaptive procedure for the numerical solution of general, semilinear elliptic boundary value problems in 1d, with possible singular perturbations.…