Kristoffer van der Zee

Contact

• workRoom C42 Mathematical Sciences Building
  University Park
  Nottingham
  NG7 2RD
  UK
• work0115 8467914
• KG.vanderZee@nottingham.ac.uk

Biography

• Full Professor of Numerical Analysis & Computational Applied Mathematics, School of Mathematical Sciences, University of Nottingham (since Aug 2023)
• Director of Automation Innovation, School of Mathematical Sciences, University of Nottingham (since Aug 2023)
• Interim PGR Student Advisor, School of Mathematical Sciences, University of Nottingham (since Aug 2023)
• Director of PGR Studies, School of Mathematical Sciences, University of Nottingham (Aug 2020-2023)
• Associate Professor of Scientific Computation, School of Mathematical Sciences, University of Nottingham (Aug 2020 - Aug 2023)
• Editor, Engineering with Computers, since Oct 2023 (Associate Editor, Sep 2021 - Sep 2023).
• Associate Fellow of the Higher Education Academy (AFHEA) (since 2018).
• Nottingham SIAM-IMA Student Chapter Faculty Advisor, inaugural (Nov 2017 - Aug 2020)
• Royal Society Kan Tong Po International Exchange Fellow, City University of Hong Kong (Nov 2015 - Jan 2016)
• School PGR Student Advisor, School of Mathematical Sciences, University of Nottingham (Aug 2015 - Aug 2020)
• Nottingham Node Representative MAGIC (Mathematics Access Grid: Instruction and Collaboration) (Aug 2015 - Aug 2020)
• Lecturer (Assistant Prof) of Scientific Computation, School of Mathematical Sciences, University of Nottingham (Oct 2013 - Aug 2020)

Other biography

• Feb 2011 - Oct 2013 :: Assistant Professor (NWO Veni Early Career Fellow), Multiscale Engineering Fluid Dynamics, Dept Mathematics & Computer Science and Mechanical Engineering, Eindhoven University of Technology
• July 2009 - Jan 2011 :: Postdoctoral Researcher, Multiscale Modeling Group, Institute for Computational Engineering and Sciences, The University of Texas at Austin
• June 2009 :: PhD Degree, Delft University of Technology (PhD Thesis: -Link1- Goal-Adaptive Discretization of Fluid-Structure Interaction)
• Oct 2004 :: MSc Degree, Aerospace Engineering, Delft University of Technology (MSc Thesis: An H¹(P^h)-Coercive Discontinuous Galerkin Formulation for The Poisson Problem: 1-D Analysis)

Research Summary

• Numerical analysis, scientific computation, and computational PDEs;
• Neural networks and machine-learning for scientific computation;
• Optimal discretisation theory, minimal residual (MRes) and Petrov-Galerkin methods;
• Foundations of error estimation and optimality of adaptive FEM;
• Reduced-order, multi-scale, and adaptive modelling;
• Uncertainty quantification, validation and optimal Bayesian experimental design;
• Evolving-interface phenomena, free- and moving-boundary problems;
• Multiphase flows and materials, and phase-field/diffuse-interface models;
• Applications to fluid dynamics, mechanobiology and engineering mechanics.

Member of School of Mathematical Sciences' Research Themes and Centres

• Research Theme Computational Statistics and Machine Learning
• Research Theme Data-driven Modelling and Computation
• Research Theme Fluid Mechanics
• Research Theme Multiscale Modelling and Heterogeneous Media
• Research Theme Numerical and Applied Analysis
• Research Theme Wave Modelling
• Centre for Mathematical Medicine and Biology

Some recent talks

• Neural Networks for PDEs: Neural Control of FEM, Universidad de Cádiz, Programa de Doctorado en Matemáticas (2024)
• Neural Control of Finite Element Methods, LMS Research School, Adaptive Methods and Model Reduction for PDEs (2023)
• Unification of Navier-Stokes Cahn-Hilliard models with non-matching densities, Workshop, MathGeo: Phase-Field Models for Geoenergy Applications (2022)
• Computational Phase-Field Modelling, UKACM 2022 School, UK Association for Computational Mechanics (2022)
• Minimal Residual (MinRes) Finite Element Methods in Banach Spaces, Australian Seminar Series on Computational Mathematics (2021)
• Quasi-incompressible Navier-Stokes-Cahn-Hilliard systems: Thermodynamic consistency and stable schemes, Workshop, Phase 2019: Engineering to Biology, University of Pavia (2019)

Organiser

• 15-19 May 2023: LMS Research School Adaptive Methods and Model Reduction for PDEs (http://www.tinyurl.com/wuwmc2kp)
• 29 June 2022: Seminar Numerical & Applied Analysis, speaker Prof Ignacio Muga (Pontificia Universidad Católica de Valparaíso, Chile), supported by LMS Scheme 2 grant
• 20-22 April 2022: Conference UKACM 2022, https://www.ukacm2022.ukacm.org/
• 25-26 April 2019: Workshop, Scientific computation using machine-learning algorithms: Recent mathematical advances and applications

Postgraduate Projects

• Please contact me if you're interested in pursuing a postgraduate degree in one of the above research topics! Also have a look at our School's Postgraduate Projects, Online Application Details and Funding Details.

Postdoctoral opportunities (general UK fellowships)

• RC1851 Fellowship
• RS Newton International Fellowship
• Nottingham Research Fellowship
• Leverhulme Fellowship

Teaching Summary

2023-2024

• MATH2019 - Introduction to Scientific Computation (autumn semester) (Link to Catalogue)
• MAGIC098 - Adaptive Finite Element Methods (autumn semester) (Link to MAGIC website)
• MATH3036 - Scientific Computation and Numerical Analysis (spring semester) (Link to Catalogue)

2022-2023

• MATH2019 - Introduction to Scientific Computation (autumn semester) (Link to Catalogue)
• MAGIC098 - Adaptive Finite Element Methods (autumn semester) (Link to MAGIC website)
• MATH3036 - Scientific Computation and Numerical Analysis (spring semester) (Link to Catalogue)

2021-2022

• MATH2019 (G12ISC) - Introduction to Scientific Computation (autumn semester) (Link to Catalogue)

2020-2021

• MATH2019 (G12ISC) - Introduction to Scientific Computation (autumn semester) (Link to Catalogue)
• MATH4064 (G14CAM) - Computational Applied Mathematics (Link to Catalogue)

2019-2020

• MATH2019 (G12ISC) - Introduction to Scientific Computation (autumn semester) (Link to Catalogue)
• MATH4064 (G14CAM) - Computational Applied Mathematics (Link to Catalogue)

2018-2019

• MATH2019 (G12ISC) - Introduction to Scientific Computation (autumn semester) (Link to Catalogue)

2017-2018

• G12ISC - Introduction to Scientific Computation (spring semester) (Link to Catalogue)
• G14CAM - Computational Applied Mathematics (Link to Catalogue)

2016-2017

• G12ISC - Introduction to Scientific Computation (spring semester) (Link to Catalogue)
• G14CAM - Computational Applied Mathematics (Link to Catalogue)
• Advanced Discretization: Theory, Applications and Numerical Implementation (part of Doctoral School in Mathematics, Valparaiso, Chile)

2015-2016

• G12INM / HG2INM - Introduction to Numerical Methods (spring semester) (Link to Catalogue)
• G14CAM - Computational Applied Mathematics (Link to Catalogue)

2014-2015

• G12INM / HG2INM - Introduction to Numerical Methods (spring semester) (Link to Catalogue and Moodle)
• HG4MPD (UK) - Mathematical Techniques in PDEs for Engineers (Link to Catalogue and Moodle)

2013-2014

• HG4MPD (UK) - Mathematical Techniques in PDEs for Engineers (Link to Catalogue and Moodle)
• Introduction to Phase-Field Modeling (part of EM school short-course on Adv. Topics Solid Mech.)

2012-2013

• Interfaces and Free Boundaries: Modeling and Computation (Notes contents; TU/e MSc class)
• Advanced Discretization Techniques (Notes contents; TU/e MSc class)
• Goal-Oriented Methods: Error Estimation, Adaptive Algorithms, Multiscale Modeling (USACM short course)

2011-2012

• Advanced Discretization Techniques (Notes contents; TU/e MSc class)
• Fundamentals of Fluid-Structure Interaction (TU/e MSc class)
• Shape Calculus (part of ECCAM school short-course on Isogeometric Analysis)
• Introduction to Phase-Field Modeling (part of EM school short-course on Adv. Topics Solid Mech.)

2010, 2011

• Goal-Oriented Methods: Error Estimation, Adaptive Algorithms, Multiscale Modeling (USACM short course)
• Introduction to Phase-Field Modeling and the Cahn-Hilliard Equation (part of EM school short-course on Adv. Topics Solid Mech.)

Supervision

• Ignacio Brevis (Postdoc), Topic: Scientific Machine Learning for membrane manufacturing, 2022-2025
• Tanakorn Udomworarat, Topic: Scientific Machine Learning for wave modelling, PhD project 2022-2026
• Sattam Alrashidy, Topic: Optimisation, control and estimation for nonlinear PDEs with applications in Fluid Mechanics, PhD project 2021-2024
• Hamd Alsobhi, Topic: Optimisation algorithms for Minimal-Residual FEM, PhD project 2020-2023
• Xuesi (Rose) Yang, Zhengyuan (Cassie) Zhang, Yu (Summer) Qi, Zeqi (Elain) Wang, Geometric Modelling of Human Bodies, UG Summer 2020
• Anne Boschman, Topic: Bulk-surface phase-field modelling, PhD project 2019-2023
• Isil Akpinar (Postdoc), Topic: Machine Learning for Membrane Manufacturing, 2019-2021
• Connor Rourke (2nd supervisor), Topic: Adaptive FEM, PhD project 2019-2023
• Yiyun Fan (2nd supervisor), Topic: Two-fluid flow asymptotics, PhD project 2019-2022
• Toby Willis (with Matteo Icardi), Diffuse-domain approximations for porous media flow, UG Summer 2019, Nottingham
• Matthew Tyler (with Donald Brown), Advanced discontinuous discretisation techniques for multiscale PDEs, Summer 2018 (LMS Undergraduate Bursary), Nottingham
• Sarah Roggendorf, Topic: Adaptive FEM for nonlinear PDEs, PhD project 2016-2019, University of Nottingham
• Yuchen Yang (2nd supervisor), Topic: Bayesian inference for PDEs, PhD project 2015-2018, University of Nottingham (VC Scholarship for Research Excellence)
• Chris Miles, Topic: Solar-cell computational phase-field modelling, PhD project 2015-2019, University of Nottingham
• Holly Smith (2nd supervisor), Topic: Tumour pattern formation, PhD project 2015-2018, University of Nottingham
• Lee Curtin (2nd supervisor), Topic: Mathematical modelling of brain tumour growth and therapy, 30 April 2019, University of Nottingham
• Xunxun Wu, Space-time adaptive methods for phase-field models, 28 June 2017, Eindhoven University of Technology
• Gorkem Simsek, Numerical methods for diffuse interface models of binary flows, 21 June 2017, Eindhoven University of Technology
• Benjamin Dominguez, Modelling error estimation for granular solids, MSc thesis 2015, University of Nottingham
• James Malone, Truncation-induced error estimation for the Black-Scholes model, MSc thesis 2015, University of Nottingham
• Ian Roper, Partitioned-domain concurrent multiscale modelling, Master's thesis 2015, University of Nottingham
• Panagiotis Zacharis, Bayesian calibration and model selection for elastic continua, MSc thesis 2014, University of Nottingham
• Jack Litherland, Topic: Particle-continuum multiscale modeling, 2014 BSc Summer Studentship (Dean's Fund), University of Nottingham
• Rody van Tuijl, Energy stable discretisation of surfactant transport on fluid surfaces, MSc thesis 2013, Eindhoven University of Technology
• Göktürk Kuru, Goal-adaptive isogeometric analysis with hierarchical splines, MSc thesis 2013, Eindhoven University of Technology
• Peter Fick, Goal-oriented a-posteriori error estimation and adaptivity for fluid-structure interaction, MSc thesis 2008, Delft University of Technology
• Ted Heemskerk, Discontinuous Galerkin methods with solenoidal elements for the Stokes problem, MSc thesis 2006, Delft University of Technology

Preprints

• A. Boschman, L. Espath, K.G. van der Zee, A bulk-surface continuum theory for fluid flows and phase segregation with finite surface thickness, arXiv:2308.01647
• Y. Fan, J. Billingham, K.G. van der Zee, A shape-Newton method for free-boundary problems subject to the Bernoulli boundary condition, arXiv:2305.14254, 2023
• Sferza, Ninic, Glock, Hofer, Daoud, Chronopoulos, Van der Zee, Global-local multidisciplinary optimisation for the evaluation of local constraints on finer meshes in preliminary aircraft design, Engineering with Computers, to appear
• I. Brevis, I. Muga, D. Pardo, O. Rodriguez, K.G. van der Zee, Learning quantities of interest from parametric PDEs: An efficient neural-weighted Minimal Residual approach, arXiv:2304.01722, 2023
• M. ten Eikelder, K.G. van der Zee, D. Schillinger, Thermodynamically consistent diffuse-interface mixture models of incompressible multicomponent fluids, arXiv:2302.09287, 2023
• I. Brevis, I. Muga, K.G. van der Zee, Neural Control of Discrete Weak Formulations: Galerkin, Least-Squares & Minimal-Residual Methods with Quasi-Optimal Weights. Computer Methods in Applied Mechanics and Engineering, to appear. See also: arXiv:2206.07475
• P. Houston, C. Rourke, K.G. van der Zee, Linearisation of the Travel Time functional in porous media flows, SIAM J. Scientific Computing, to appear. 10.1137/21M1451105, See also: arXiv:2111.15504
• M. ten Eikelder, K.G. van der Zee, I. Akkerman, D. Schillinger, Unified framework for Navier-Stokes Cahn-Hilliard models with non-matching densities, Mathematical Models and Methods in Applied Sciences (to appear), See also: arXiv:2110.11912
• F. Millar, I. Muga, S. Rojas, K.G. van der Zee, Projection in negative norms and the regularization of rough linear functionals, Numerische Mathematik, 150, pages 1087-1121 (2022). See also: arXiv:2101.03044
• P. HOUSTON, S. ROGGENDORF, K.G. VAN DER ZEE, Gibbs Phenomena for Lq-Best Approximation in Finite Element Spaces, ESAIM: Mathematical Modelling and Numerical Analysis, (2022) 177-211, 10.1051/m2an/2021086. See also: arXiv:1909.00658
• K.G. VAN DER ZEE, S. PRUDHOMME, J.T. ODEN, Adaptive modeling for partitioned-domain concurrent multiscale continuum models
• Publications at Google scholar

Selected Publications

• A. BOSCHMAN, L. ESPATH and K.G. VAN DER ZEE, 2024. A bulk-surface continuum theory for fluid flows and phase segregation with finite surface thickness Physica D: Nonlinear Phenomena. (In Press.)
• I. BREVIS, I.M. MUGA and K.G. VAN DER ZEE, 2023. Neural Control of Discrete Weak Formulations: Galerkin, Least Squares & Minimal-Residual Methods with Quasi-Optimal Weights Computer Methods in Applied Mechanics and Engineering. (In Press.)
• M.F.P. TEN EIKELDER, K.G. VAN DER ZEE, I. AKKERMAN and D. SCHILLINGER, 2023. A unified framework for Navier-Stokes Cahn-Hilliard models with non-matching densities Mathematical Models and Methods in Applied Sciences. (In Press.)
• NINIC, J., VAN DER ZEE, K.G., ICARDI, M. and WANG, F., 2023. Editorial UKACM 2022: advances in computational mechanics Engineering with Computers: An International Journal for Simulation-Based Engineering.

• View all publications

• A. BOSCHMAN, L. ESPATH and K.G. VAN DER ZEE, 2024. A bulk-surface continuum theory for fluid flows and phase segregation with finite surface thickness Physica D: Nonlinear Phenomena. (In Press.)
• I. BREVIS, I.M. MUGA and K.G. VAN DER ZEE, 2023. Neural Control of Discrete Weak Formulations: Galerkin, Least Squares & Minimal-Residual Methods with Quasi-Optimal Weights Computer Methods in Applied Mechanics and Engineering. (In Press.)
• M.F.P. TEN EIKELDER, K.G. VAN DER ZEE, I. AKKERMAN and D. SCHILLINGER, 2023. A unified framework for Navier-Stokes Cahn-Hilliard models with non-matching densities Mathematical Models and Methods in Applied Sciences. (In Press.)
• NINIC, J., VAN DER ZEE, K.G., ICARDI, M. and WANG, F., 2023. Editorial UKACM 2022: advances in computational mechanics Engineering with Computers: An International Journal for Simulation-Based Engineering.
• M. SFERZA, J. NINIC, F. GLOCK, C. HOFER, F. DAOUD, D. CHRONOPOULOS and K. VAN DER ZEE, 2023. Global–local multidisciplinary optimisation for the evaluation of local constraints on finer meshes in preliminary aircraft design Engineering with Computers: An International Journal for Simulation-Based Engineering. 39(6), 4167-4184
• P. HOUSTON, S. ROGGENDORF and K.G. VAN DER ZEE, 2022. Gibbs Phenomena For L^q-best Approximation in Finite Element Spaces ESAIM Mathematical Modelling and Numerical Analysis. 56, 177-211
• F. MILLAR, I. MUGA, S. ROJAS and K.G. VAN DER ZEE, 2022. Projection in negative norms and the regularization of rough linear functionals Numerische Mathematik. (In Press.)
• P. HOUSTON, C.J. ROURKE and K.G. VAN DER ZEE, 2022. Linearisation of the Travel Time Functional in Porous Media Flows SIAM Journal of Scientific Computing. (In Press.)
• J. ZHANG, JOHN EVANS, H. GOMEZ and K. VAN DER ZEE, 2022. An editorial perspective: new team, aims and scope and advances of EWCO Engineering with Computers. 38, 1
• IGNACIO BREVIS, IGNACIO MUGA and KRISTOFFER G VAN DER ZEE, 2021. A machine-learning minimal-residual (ML-MRes) framework for goal-oriented finite element discretizations Computers and Mathematics with Applications. 95, 186-199
• LEE CURTIN, ANDREA HAWKINS-DAARUD, KRISTOFFER G VAN DER ZEE, KRISTIN R SWANSON and MARKUS R OWEN, 2020. Speed switch in glioblastoma growth rate due to enhanced hypoxia-induced migration Bulletin of Mathematical Biology. 82(3), 43
• PAUL HOUSTON, SARAH ROGGENDORF and KRISTOFFER G VAN DER ZEE, 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
• LEE CURTIN, ANDREA HAWKINS-DAARUD, ALYX B. PORTER, KRISTOFFER G. VAN DER ZEE, MARKUS R. OWEN and KRISTIN R. SWANSON, 2020. A Mechanistic Investigation into Ischemia-Driven Distal Recurrence of Glioblastoma Bulletin of Mathematical Biology. 82, 143
• IGNACIO MUGA and KRISTOFFER G. VAN DER ZEE, 2020. Discretization of Linear Problems in Banach Spaces: Residual Minimization, Nonlinear Petrov-Galerkin, and Monotone Mixed Methods SIAM Journal in Numerical Analysis. 58(6), 3406-3426
• JUDITH MUÑOZ-MATUTE, VICTOR M CALO, DAVID PARDO, ELISABETE ALBERDI and KRISTOFFER G VAN DER ZEE, 2019. Explicit-in-Time Goal-Oriented Adaptivity Computer Methods in Applied Mechanics and Engineering. 347, 176-200
• CHRISTOPHER MILES, KRISTOFFER G VAN DER ZEE, MATTHEW E HUBBARD and RODERICK MACKENZIE, 2019. Chapter 11 Thermomechanically-Consistent Phase-Field Modeling of Thin Film Flows. In: E.H. VAN BRUMMELEN, A. CORSINI, S. PEROTTO and G. ROZZA, eds., Numerical Methods for Flows: FEF 2017 Selected Contributions. Lecture Notes in Computational Science and Engineering https://www.springer.com/gp/book/9783030307042 132. Springer.
• P. HOUSTON, I. MUGA, S. ROGGENDORF and K.G. VAN DER ZEE, 2019. The convection-diffusion-reaction equation in non-Hilbert Sobolev spaces: A direct proof of the inf-sup condition and stability of Galerkin's method Computational Methods in Applied Mathematics. 19(3), 503-522
• I. MUGA, M.J.W. TYLER and K.G. VAN DER ZEE, 2019. The Discrete-Dual Minimal-Residual Method (DDMRes) for Weak Advection-Reaction Problems in Banach spaces Computational Methods in Applied Mathematics. 19(3), 557-579
• R. DYJA, B. GANAPATHYSUBRAMANIAN and K.G. VAN DER ZEE, 2018. Parallel-in-space-time, adaptive finite element framework for non-linear parabolic equations SIAM Journal on Scientific Computing: Software and High-Performance Computing. 40(3), C283–C304
• M. SHOKRPOUR-ROUDBARI, G. SIMSEK, E.H VAN BRUMMELEN and K.G. VAN DER ZEE, 2018. Diffuse-interface two-phase flow models with different densities: A new quasi-incompressible form and a linear energy-stable method Mathematical Models and Methods in Applied Sciences. 28(4), 733–770
• X. WU, K.G. VAN DER ZEE, G. SIMSEK and E.H. VAN BRUMMELEN, 2018. A-posteriori error estimation and adaptivity for nonlinear parabolic equations using IMEX-Galerkin discretization of primal and dual equations SIAM Journal on Scientific Computing: Methods and Algorithms for Scientic Computing. 40(5), A3371-A3399
• E.H. VAN BRUMMELEN, M. SHOKRPOUR ROUDBARI, G. SIMSEK and K.G. VAN DER ZEE, 2017. Binary-fluid-solid interaction based on the Navier-Stokes-Cahn-Hilliard Equations. In: Fluid-Structure Interaction: Modeling, Adaptive Discretisations and Solvers De Gruyter, Vol 20 of Radon Series on Computational and Applied Mathematics.
• H. GOMEZ and K.G. VAN DER ZEE, 2017. Computational Phase-Field Modeling. In: E. STEIN, R. DE BORST and T.J.R. HUGHES, eds., Encyclopedia of Computational Mechanics, 2nd Edition: Wiley, https://onlinelibrary.wiley.com/doi/book/10.1002/9781119176817
• M. FEISCHL, D. PRAETORIUS and K.G. VAN DER ZEE, 2016. An abstract analysis of optimal goal-oriented adaptivity SIAM Journal of Numerical Analysis. 54(3), 1423-1448
• I. MUGA and K.G. VAN DER ZEE, 2016. Adaptive discretization in Banach spaces with the nonlinear Petrov-Galerkin method: in Adaptive Algorithms, C. Carstensen, R. Stevenson, eds. Oberwolfach Reports. 13(3), 2562-2564
• D. HILHORST, J. KAMPMANN, T.N. NGUYEN and K.G. VAN DER ZEE, 2015. Formal asymptotic limit of a diffuse-interface tumor-growth model Mathematical Models and Methods in Applied Sciences. 25(6), 1011-1044
• G. SIMSEK, X. WU, K.G. VAN DER ZEE and E.H. VAN BRUMMELEN, 2015. Duality-based two-level error estimation for time-dependent PDEs: Application to linear and nonlinear parabolic equations Computer Methods in Applied Mechanics and Engineering. 288, 83-109
• M. LAFOREST, S. PRUDHOMME and K.G. VAN DER ZEE, 2015. Preface to the special issue on error estimation and adaptivity for nonlinear and time-dependent problems Computer Methods in Applied Mechanics and Engineering. 288, 1
• WU, X., VAN ZWIETEN, G. J. and VAN DER ZEE, K. G., 2014. Stabilized second-order convex splitting schemes for Cahn–Hilliard models with application to diffuse-interface tumor-growth models INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN BIOMEDICAL ENGINEERING. 30(2), 180-203
• G. KURU, C.V. VERHOOSEL, K.G. VAN DER ZEE and E.H. VAN BRUMMELEN, 2014. Goal-adaptive Isogeometric Analysis with hierarchical splines Computer Methods in Applied Mechanics and Engineering. 270, 270-292
• G.J. VAN ZWIETEN, E.H. VAN BRUMMELEN, K.G. VAN DER ZEE, M.A. GUTIÉRREZ and R.F. HANSSEN, 2014. Discontinuities without discontinuity: The Weakly-enforced Slip Method Computer Methods in Applied Mechanics and Engineering. 271, 144-166
• GARG, V.V., PRUDHOMME,. S., VAN DER ZEE, K.G. and CAREY, G.F., 2014. Adjoint-consistent formulations of slip models for coupled electroosmotic flow systems Advanced Modeling and Simulation in Engineering Sciences. 2, 15
• A. HAWKINS-DAARUD, J.T. ODEN, S. PRUDHOMME and K.G. VAN DER ZEE, 2014. A four-species diffuse-interface tumor-growth model of gradient-flow type: in Reactive Flows in Deformable, Complex Media, M. Gerritsen, J. Nordbotten, I. Pop, B. Wohlmuth, eds. Oberwolfach Reports. 11(3), 2424-2426
• HAWKINS-DAARUD, A., PRUDHOMME, S., VAN DER ZEE, K. G. and ODEN, J.T., 2013. Bayesian calibration, validation, and uncertainty quantification of diffuse interface models of tumor growth JOURNAL OF MATHEMATICAL BIOLOGY. 67(6-7), 1457-1485
• VAN DER ZEE, K. G., VAN ZWIETEN, G. J., VERHOOSEL, C. V. and VAN BRUMMELEN, E. H., 2013. Shape-Newton method for isogeometric discretizations of free-boundary problems. In: ECA, L., ONATE, E., GARCIA-ESPINOSA, J. and KVAMSDAL, T., eds., MARINE 2011, IV International Conference on Computational Methods in Marine Engineering: Selected Papers 29. Springer Netherlands. 85-102
• VAN BRUMMELEN, E. H., VAN DER ZEE, K. G., GARG, V. V. and PRUDHOMME, S., 2012. Flux evaluation in primal and dual boundary-coupled problems JOURNAL OF APPLIED MECHANICS-TRANSACTIONS OF THE ASME. 79(1),
• HAWKINS-DAARUD, A., VAN DER ZEE, K. G. and ODEN, J. T., 2012. Numerical simulation of a thermodynamically consistent four-species tumor growth model INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN BIOMEDICAL ENGINEERING. 28(1), 3-24
• VAN DER ZEE, K. G. and VERHOOSEL, C. V., 2011. Isogeometric analysis-based goal-oriented error estimation for free-boundary problems FINITE ELEMENTS IN ANALYSIS AND DESIGN. 47(6), 600-609
• VAN DER ZEE, K.G., VAN BRUMMELEN, E.H., AKKERMAN, I. and DE BORST, R., 2011. Goal-oriented error estimation and adaptivity for fluid-structure interaction using exact linearized adjoints Computer Methods in Applied Mechanics and Engineering. 200(37-40), 2738-2757
• VAN DER ZEE, K.G., ODEN, J.T., PRUDHOMME, S. and HAWKINS-DAARUD, A., 2011. Goal-oriented error estimation for Cahn-Hilliard models of binary phase transition Numerical Methods for Partial Differential Equations. 27(1), 160-196
• AKKERMAN, I., HULSHOFF, S. J., VAN DER ZEE, K. G. and DE BORST, R., 2011. Variational Germano approach for multiscale formulations. In: DE BORST, R. and RAMM, R., eds., Multiscale Methods in Computational Mechanics: Progress and Accomplishments 55. Springer Netherlands. 53-73
• VAN DER ZEE, K.G., VAN BRUMMELEN, E.H. and DE BORST, R., 2010. Goal-oriented error estimation and adaptivity for free-boundary problems: the domain-map linearization approach SIAM Journal on Scientific Computing. 32(2), 1064-1092
• AKKERMAN, I., VAN DER ZEE, K. G. and HULSHOFF, S. J., 2010. A variational Germano approach for stabilized finite element methods COMPUTER METHODS IN APPLIED MECHANICS AND ENGINEERING. 199(9-12), 502-513
• VAN DER ZEE, K. G., VAN BRUMMELEN, E. H. and DE BORST, R., 2010. Goal-oriented error estimation and adaptivity for free-boundary problems: The shape-linearization approach SIAM JOURNAL ON SCIENTIFIC COMPUTING. 32(2), 1093-1118
• FICK, P. W., VAN BRUMMELEN, E. H. and VAN DER ZEE, K. G., 2010. On the adjoint-consistent formulation of interface conditions in goal-oriented error estimation and adaptivity for fluid-structure interaction COMPUTER METHODS IN APPLIED MECHANICS AND ENGINEERING. 199(49-52), 3369-3385
• VAN DER ZEE, K. G., VAN BRUMMELEN, E. H. and DE BORST, R., 2008. Goal-oriented error estimation for Stokes flow interacting with a flexible channel INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN FLUIDS. 56(8), 1551-1557
• VAN BRUMMELEN, E.H., VAN DER ZEE, K.G. and DE BORST, R., 2008. Space/time multigrid for a fluid-structure-interaction problem Applied Numerical Mathematics. 58(12), 1951-1971
• VAN DER ZEE, K. G., VAN BRUMMELEN, E. H. and DE BORST, R., 2006. An H-1(rho(h))-coercive discontinuous Galerkin formulation for the poisson problem: 1d analysis SIAM JOURNAL ON NUMERICAL ANALYSIS. 44(6), 2671-2698
• FARHAT, C., VAN DER ZEE, K. G. and GEUZAINE, P., 2006. Provably second-order time-accurate loosely-coupled solution algorithms for transient nonlinear computational aeroelasticity COMPUTER METHODS IN APPLIED MECHANICS AND ENGINEERING. 195(17-18), 1973-2001