A Sobolev gradient of a real-valued functional on a Hilbert space is a gradient of that
functional taken relative to an underlying Sobolev norm. This book shows how descent …

We extend the theory of Sobolev gradients to include variable metric methods, such as
Newton's method and the Levenberg–Marquardt method, as gradient descent iterations …

The aim of this paper is to develop stepwise variable preconditioning for the iterative
solution of monotone operator equations in Hilbert space and apply it to nonlinear elliptic …

Least squares methods are effective for solving systems of partial differential equations. In
the case of nonlinear systems the equations are usually linearized by a Newton iteration or …

In this the window of the Sobolev gradient technique to the problem of minimizing a
Schrödinger functional associated with a nonlinear Schrödinger equation. We show that …

Mahavier and Montgomery construct a Sobolev space for approximate solution of linear
initial value problems in a finite difference setting in single-iteration sobolev descent for …

Approximating time evolution related to Ginzburg–Landau functionals via Sobolev gradient
methods in a finite-element setting - ScienceDirect Skip to main contentSkip to article Elsevier …

The Sobolev gradient technique has been discussed previously in this journal as an efficient
method for finding energy minima of certain Ginzburg–Landau type functionals [S. Sial, J …

To find the minima of an energy functional, is a well known problem in physics and
engineering. Sobolev gradients have proven to be affective to find the critical points of a …

The nonlinear Klein‐Gordon equation (KGE) models many nonlinear phenomena. In this
paper, we propose a scheme for numerical approximation of solutions of the one …