Solutions to many partial differential equations satisfy certain bounds or constraints. For
example, the density and pressure are positive for equations of fluid dynamics, and in the …

In this paper, we propose and analyze a second order accurate in time, mass lumped mixed
finite element scheme for the Cahn-Hilliard equation with a logarithmic Flory-Huggins …

The well-suited discretization of the Keller–Segel equations for chemotaxis has become a
very challenging problem due to the convective nature inherent to them. This paper aims to …

This paper proposes a linear, unconditionally energy-stable scheme for the Poisson–Nernst–
Planck (PNP) equations. Based on a gradient-flow formulation of the PNP equations, the …

In this paper, linear multi-step methods are used to numerically solve gradient flow models,
and the relations between different numerical stabilities (eg, unconditional energy stability, A …

Phase-field surfactant model with moving contact lines (PFS-MCL) has been extensively
investigated in the study of droplet dynamics on solid surfaces in the presence of surfactants …

This article focuses on the convergence analysis for a fully discrete finite difference scheme
for the time-dependent Poisson–Nernst–Planck system. The numerical scheme, a three …

In this paper, we consider the linearized backward Euler finite element scheme for the
Navier-Stokes-Poisson-Nernst-Planck (NSPNP) equations. We aim to derive the …

We propose in this paper efficient first/second-order time-stepping schemes for the
evolutional Navier-Stokes-Nernst-Planck-Poisson equations. The proposed schemes are …

In this paper, we consider a linearized BDF2 finite element scheme for the Poisson–Nernst–
Planck (PNP) equations. By employing a novel approach, we rigorously derive …