Hydrogels are highly water-swollen molecular networks that are ideal platforms to create
tissue mimetics owing to their vast and tunable properties. As such, hydrogels are promising …

Mathematical modelling approaches have become increasingly abundant in cancer
research. The complexity of cancer is well suited to quantitative approaches as it provides …

Essentially non-oscillatory (ENO) and weighted ENO (WENO) schemes were designed for
solving hyperbolic and convection–diffusion equations with possibly discontinuous solutions …

Despite major scientific, medical and technological advances over the last few decades, a
cure for cancer remains elusive. The disease initiation is complex, and including initiation …

Simulating cancer behavior across multiple biological scales in space and time, ie,
multiscale cancer modeling, is increasingly being recognized as a powerful tool to refine …

In this paper we develop an evolution of the C^1 virtual elements of minimal degree for the
approximation of the Cahn--Hilliard equation. The proposed method has the advantage of …

We propose a new Lagrange multiplier approach to design unconditional energy stable
schemes for gradient flows. The new approach leads to unconditionally energy stable …

For the time-fractional phase-field models, the corresponding energy dissipation law has not
been well studied on both the continuous and the discrete levels. In this work, we address …

This book aims to introduce students and scientists to the programming of the phase-field
method. The codes provided in the book will serve as a foundation and template for …

Using basic thermodynamic principles we derive a Cahn–Hilliard–Darcy model for tumour
growth including nutrient diffusion, chemotaxis, active transport, adhesion, apoptosis and …