A numerical energy reduction approach for semilinear diffusion-reaction boundary value problems based on steady-state iterations

M Amrein, P Heid, TP Wihler - SIAM Journal on Numerical Analysis, 2023 - SIAM
We present a novel energy-based numerical analysis of semilinear diffusion-reaction
boundary value problems, where the nonlinear reaction terms need to be neither monotone …

A numerical energy minimisation approach for semilinear diffusion-reaction boundary value problems based on steady state iterations

M Amrein, P Heid, TP Wihler - arXiv preprint arXiv:2202.07398, 2022 - arxiv.org
We present a novel energy-based numerical analysis of semilinear diffusion-reaction
boundary value problems. Based on a suitable variational setting, the proposed …

On Numerical Solutions for a Class of Relativistic Quasilinear Schrödinger Equations

C Huang, Y Wang - Bulletin of the Iranian Mathematical Society, 2024 - Springer
We study the numerical solutions for a class of quasilinear Schrödinger equations arising
from the self-channeling of high-power ultra short lasers in matter, which are associated with …

Gradient flow finite element discretisations with energy-based adaptivity for excited states of Schr\" odingers equation

P Heid - arXiv preprint arXiv:2010.10383, 2020 - arxiv.org
We present an effective numerical procedure, which is based on the computational scheme
from [Heid et al., arXiv: 1906.06954], for the numerical approximation of excited states of …