Kristoffer G. van der Zee

TL;DR: In this paper, a second-order time-accurate and yet loosely-coupled partitioned procedure for the solution of nonlinear fluid-structure interaction (FSI) problems on moving grids is presented.

TL;DR: A thermodynamically consistent four-species model of tumor growth on the basis of the continuum theory of mixtures, unique to this model is the incorporation of nutrient within the mixture as opposed to being modeled with an auxiliary reaction-diffusion equation.

TL;DR: This work attempts to lay out a framework, based on Bayesian probability, for systematically addressing the questions of Validation, the process of investigating the accuracy with which a mathematical model is able to reproduce particular physical events, and Uncertainty quantification, developing measures of the degree of confidence withWhich a computer model predicts particular quantities of interest.

TL;DR: The phase-field model as discussed by the authors is a methodology to reformulate interface problems as equations posed on fixed domains, and it is shown to converge to the moving-boundary problem as a regularization parameter tends to zero, which shows the mathematical soundness of the approach.

TL;DR: In this article, a posteriori estimates of errors in quantities of interest are developed for the nonlinear system of evolution equations embodied in the Cahn-Hilliard model of binary phase transition.