All Outputs (22)

Formal asymptotic limit of a diffuse-interface tumor-growth model (2015)
Journal Article
Hilhorst, D., Kampmann, J., Nguyen, T. N., & van der Zee, K. (2015). Formal asymptotic limit of a diffuse-interface tumor-growth model. Mathematical Models and Methods in Applied Sciences, 25(6), https://doi.org/10.1142/S0218202515500268

We consider a diffuse-interface tumor-growth model which has the form of a phase-field system. We characterize the singular limit of this problem. More precisely, we formally prove that as the coefficient of the reaction term tends to infinity, the s... Read More about Formal asymptotic limit of a diffuse-interface tumor-growth model.

Duality-based two-level error estimation for time-dependent PDEs: application to linear and nonlinear parabolic equations (2014)
Journal Article
Şimşek, G., Wu, X., van der Zee, K., & van Brummelen, E. (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, https://doi.org/10.1016/j.cma.2014.11.019

We introduce a duality-based two-level error estimator for linear and nonlinear time-dependent problems. The error measure can be a space-time norm, energy norm, final-time error or other error related functional. The general methodology is developed... Read More about Duality-based two-level error estimation for time-dependent PDEs: application to linear and nonlinear parabolic equations.