This book discusses classical results, as well as recent developments, related to the Cahn–
Hilliard equation. It is based on the lectures that I gave at the CBMS-NSF Conference on the …

Abstract The Cahn-Hilliard phase-field model of two-phase incompressible flows, namely
the Cahn-Hilliard-Navier-Stokes (CH-NS) problem represents the fundamental building …

In this paper, we consider the numerical solution of damped Boussinesq equation using
Ciarlet–Raviart mixed finite element method. An implicit finite difference scheme is used for …

Cell membranes, mediator of many biological mechanisms from adhesion and metabolism
up to mutation and infection, are highly dynamic and heterogeneous environments …

In this paper, the one-and two-dimensional stochastic multi-order fractional diffusion-wave
equations are introduced and a collocation procedure based on the shifted Jacobi …

The main aim of this paper is to present new and simple numerical methods for solving the
time-dependent transport equation on the sphere in spherical coordinates. We use two …

This paper proposes a discontinuous Galerkin method to solve the generalized Sobolev
equation. In this numerical procedure, the temporal variable has been discretized by the …

We present an adaptive multilevel Monte Carlo algorithm for solving the stochastic drift–
diffusion–Poisson system with non-zero recombination rate. The a-posteriori error is …

Due to current scouring, submarine cables are prone to be exposed, suspended, and even
vortex-induced vibration, which is not conducive to the safe operation of the power grid. In …

The cavity pressure in the injection molding process is closely related to the quality of the
molded products, and is used for process monitoring and control, to upgrade the quality of …