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Professor KRISTOFFER VAN DER ZEE's Outputs (4)

Explicit-in-time goal-oriented adaptivity (2018)
Journal Article
Muñoz-Matute, J., Calo, V. M., Pardo, D., Alberdi, E., & Van Der Zee, K. (2019). Explicit-in-time goal-oriented adaptivity. Computer Methods in Applied Mechanics and Engineering, 347, 176-200. https://doi.org/10.1016/j.cma.2018.12.028

Goal-oriented adaptivity is a powerful tool to accurately approximate physically relevant solution features for Partial Differential Equations. In time dependent problems, we seek to represent the error in the quantity of interest as an integral over... Read More about Explicit-in-time goal-oriented adaptivity.

A-posteriori error estimation and adaptivity for nonlinear parabolic equations using IMEX-Galerkin discretization of primal and dual equations (2018)
Journal Article
Wu, X., van der Zee, K., Simsek, G., & van Brummelen, E. (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, 40(5), A3371–A3399. https://doi.org/10.1137/17M1133968

While many methods exist to discretize nonlinear time-dependent partial differential equations (PDEs), the rigorous estimation and adaptive control of their discretization errors remains challenging. In this paper, we present a methodology for dualit... Read More about A-posteriori error estimation and adaptivity for nonlinear parabolic equations using IMEX-Galerkin discretization of primal and dual equations.

Parallel-in-space-time, adaptive finite element framework for non-linear parabolic equations (2018)
Journal Article
Dyja, R., Ganapathysubramanian, B., & van der Zee, K. G. (in press). Parallel-in-space-time, adaptive finite element framework for non-linear parabolic equations. SIAM Journal on Scientific Computing, 40(3), Article C283-C304. https://doi.org/10.1137/16M108985X

We present an adaptive methodology for the solution of (linear and) non-linear time dependent problems that is especially tailored for massively parallel computations. The basic concept is to solve for large blocks of space-time unknowns instead of m... Read More about Parallel-in-space-time, adaptive finite element framework for non-linear parabolic equations.

Diffuse-interface two-phase flow models with different densities: A new quasi-incompressible form and a linear energy-stable method (2018)
Journal Article
Shokrpour Roudbari, M., Şimşek, G., Brummelen, E. V., & Van Der Zee, K. G. (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. https://doi.org/10.1142/S0218202518500197

© 2018 World Scientific Publishing Company. While various phase-field models have recently appeared for two-phase fluids with different densities, only some are known to be thermodynamically consistent, and practical stable schemes for their numerica... Read More about Diffuse-interface two-phase flow models with different densities: A new quasi-incompressible form and a linear energy-stable method.