All Outputs (6)

Discretization of linear problems in banach spaces: Residual minimization, nonlinear petrov-galerkin, and monotone mixed methods (2020)
Journal Article
Muga, I., & Van Der Zee, K. G. (2020). Discretization of linear problems in banach spaces: Residual minimization, nonlinear petrov-galerkin, and monotone mixed methods. SIAM Journal on Numerical Analysis, 58(6), 3406-3426. https://doi.org/10.1137/20M1324338

This work presents a comprehensive discretization theory for abstract linear operator equations in Banach spaces. The fundamental starting point of the theory is the idea of residual minimization in dual norms and its inexact version using discrete d... Read More about Discretization of linear problems in banach spaces: Residual minimization, nonlinear petrov-galerkin, and monotone mixed methods.

A Mechanistic Investigation into Ischemia-Driven Distal Recurrence of Glioblastoma (2020)
Journal Article
Curtin, L., Hawkins-Daarud, A., Porter, A. B., van der Zee, K. G., Owen, M. R., & Swanson, K. R. (2020). A Mechanistic Investigation into Ischemia-Driven Distal Recurrence of Glioblastoma. Bulletin of Mathematical Biology, 82(11), Article 143. https://doi.org/10.1007/s11538-020-00814-y

Glioblastoma (GBM) is the most aggressive primary brain tumor with a short median survival. Tumor recurrence is a clinical expectation of this disease and usually occurs along the resection cavity wall. However, previous clinical observations have su... Read More about A Mechanistic Investigation into Ischemia-Driven Distal Recurrence of Glioblastoma.

A machine-learning minimal-residual (ML-MRes) framework for goal-oriented finite element discretizations (2020)
Journal Article
Brevis, I., Muga, I., & van der Zee, K. G. (2021). A machine-learning minimal-residual (ML-MRes) framework for goal-oriented finite element discretizations. Computers and Mathematics with Applications, 95, 186-199. https://doi.org/10.1016/j.camwa.2020.08.012

We introduce the concept of machine-learning minimal-residual (ML-MRes) finite element discretizations of partial differential equations (PDEs), which resolve quantities of interest with striking accuracy, regardless of the underlying mesh size. The... Read More about A machine-learning minimal-residual (ML-MRes) framework for goal-oriented finite element discretizations.

Eliminating Gibbs phenomena: A non-linear Petrov–Galerkin method for the convection–diffusion–reaction equation (2020)
Journal Article
Houston, P., Roggendorf, S., & van der Zee, K. G. (2020). Eliminating Gibbs phenomena: A non-linear Petrov–Galerkin method for the convection–diffusion–reaction equation. Computers and Mathematics with Applications, 80(5), 851-873. https://doi.org/10.1016/j.camwa.2020.03.025

In this article we consider the numerical approximation of the convection-diffusion-reaction equation. One of the main challenges of designing a numerical method for this problem is that boundary layers occurring in the convection-dominated case can... Read More about Eliminating Gibbs phenomena: A non-linear Petrov–Galerkin method for the convection–diffusion–reaction equation.

Speed Switch in Glioblastoma Growth Rate due to Enhanced Hypoxia-Induced Migration (2020)
Journal Article
Curtin, L., Hawkins-Daarud, A., van der Zee, K. G., Swanson, K. R., & Owen, M. R. (2020). Speed Switch in Glioblastoma Growth Rate due to Enhanced Hypoxia-Induced Migration. Bulletin of Mathematical Biology, 82(3), Article 43. https://doi.org/10.1007/s11538-020-00718-x

We analyze the wave-speed of the Proliferation Invasion Hypoxia Necro-sis Angiogenesis (PIHNA) model that was previously created and applied to simulate the growth and spread of glioblastoma (GBM), a particularly aggressive primary brain tumor. We ex... Read More about Speed Switch in Glioblastoma Growth Rate due to Enhanced Hypoxia-Induced Migration.

Thermomechanically-Consistent Phase-Field Modeling of Thin Film Flows (2020)
Book Chapter
Zee, K. G. D., Zee, K. G. V. D., Miles, C., van der Zee, K. G., Hubbard, M. E., & MacKenzie, R. (2020). Thermomechanically-Consistent Phase-Field Modeling of Thin Film Flows. In H. van Brummelen, A. Corsini, S. Perotto, & G. Rozza (Eds.), Numerical methods for flows: FEF 2017 selected contributions (121-129). Springer Verlag. https://doi.org/10.1007/978-3-030-30705-9_11

© Springer Nature Switzerland AG 2020. We use phase-field techniques coupled with a Coleman–Noll type procedure to derive a family of thermomechanically consistent models for predicting the evolution of a non-volatile thin liquid film on a flat subst... Read More about Thermomechanically-Consistent Phase-Field Modeling of Thin Film Flows.