Professor KRISTOFFER VAN DER ZEE's Outputs (4)

A Shape-Newton method for free-boundary problems subject to the Bernoulli boundary condition (2024)
Journal Article
Fan, Y., Billingham, J., & van der Zee, K. (2024). A Shape-Newton method for free-boundary problems subject to the Bernoulli boundary condition. SIAM Journal on Scientific Computing, 46(6), A3599-A3627. https://doi.org/10.1137/23M1590263

We develop a shape-Newton method for solving generic free-boundary problems where one of the free-boundary conditions is governed by the nonlinear Bernoulli equation. The method is a Newton-like scheme that employs shape derivatives of the governing... Read More about A Shape-Newton method for free-boundary problems subject to the Bernoulli boundary condition.

Thermodynamically consistent diffuse-interface mixture models of incompressible multicomponent fluids (2024)
Journal Article
ten Eikelder, M. F., van der Zee, K. G., & Schillinger, D. (2024). Thermodynamically consistent diffuse-interface mixture models of incompressible multicomponent fluids. Journal of Fluid Mechanics, 990, Article A8. https://doi.org/10.1017/jfm.2024.502

The prototypical diffuse-interface model for incompressible fluid mixtures is the Navier–Stokes Cahn–Hilliard (Allen–Cahn) model. Despite its foundation in continuum mixture theory, it is not fully compatible with this theory due to the diffusive flu... Read More about Thermodynamically consistent diffuse-interface mixture models of incompressible multicomponent fluids.

Controlling ZIF-67 film properties in water-based cathodic electrochemical deposition (2024)
Journal Article
Elsayed, E., Brevis, I., Pandiyan, S., Wildman, R., van der Zee, K. G., & Tokay, B. (2024). Controlling ZIF-67 film properties in water-based cathodic electrochemical deposition. Journal of Solid State Chemistry, 338, Article 124820. https://doi.org/10.1016/j.jssc.2024.124820

One of the main approaches to increase the surface area of a substrate is through depositing a film of a porous materials such as Zeolite imidazole framework (ZIF). ZIF films have shown surpassing capabilities because of their zeolite-like features,... Read More about Controlling ZIF-67 film properties in water-based cathodic electrochemical deposition.

Learning quantities of interest from parametric PDEs: An efficient neural-weighted Minimal Residual approach (2024)
Journal Article
Brevis, I., Muga, I., Pardo, D., Rodriguez, O., & van der Zee, K. G. (2024). Learning quantities of interest from parametric PDEs: An efficient neural-weighted Minimal Residual approach. Computers and Mathematics with Applications, 164, 139-149. https://doi.org/10.1016/j.camwa.2024.04.006

The efficient approximation of parametric PDEs is of tremendous importance in science and engineering. In this paper, we show how one can train Galerkin discretizations to efficiently learn quantities of interest of solutions to a parametric PDE. The... Read More about Learning quantities of interest from parametric PDEs: An efficient neural-weighted Minimal Residual approach.