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 …

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 …

Modeling the time evolution of atomic number densities and the kinetic (non‐Maxwellian)
electron energy distribution function under the action of electron impact collisions by …

A weighted Sobolev gradient approach [1] is presented to a nonlinear PBE [2] with
discontinuous coefficient functions. A comparison is given between the weighted and …

We describe an approach to solving a generic time-dependent differential equation (DE) that
recasts the problem as a functional optimization one. The techniques employed to solve for …

The one-dimensional nonlinear Schrödinger equation (NLSE) has a wide range of
applications in nonlinear optical and laser physics. The design of new optical systems …

The idea of a weighted Sobolev gradient, introduced and applied to singular differential
equations in 1], is extended to a Poisson-Boltzmann system with discontinuous coe cients …

The application of Sobolev gradient methods for finding critical points of the Huxley and
Fisher models is demonstrated. A comparison is given between the Euclidean, weighted …

A temporal multiscale hybridization method is presented that carefully couples coarse scale
gyrokinetic models with exact charged particle solution trajectories (that is, with full phase …