15 citations · 33 across the 17 of their papers we have counts for
5 papers · 1 filter
An adaptive rectangular mesh administration and refinement technique with application in cancer invasion models
Niklas Kolbe, Nikolaos Sfakianakis
We present an administration technique for the bookkeeping of adaptive mesh refinement on (hyper-)rectangular meshes. Our technique is a unified approach for h-refinement on 1-, 2-…
Numerical simulation of a contractivity based multiscale cancer invasion model
Niklas Kolbe, Maria Lukacova-Medvidova, Nikolaos Sfakianakis +1
We present a problem-suited numerical method for a particularly challenging cancer invasion model. This model is a multiscale haptotaxis advection-reaction-diffusion system that de…
Numerical study of cancer cell invasion dynamics using adaptive mesh refinement: the urokinase model
Niklas Kolbe, Jana Katuchova, Nikolaos Sfakianakis +2
In the present work we investigate the chemotactically and proteolytically driven tissue invasion by cancer cells. The model employed is a system of advection-reaction-diffusion eq…
Entropy dissipation of moving mesh adaptation
Maria Lukacova-Medvidova, Nikolaos Sfakianakis
Non-uniform grids and mesh adaptation have been a growing part of numerical simulation over the past years. It has been experimentally noted that mesh adaptation leads not only to…
Adaptive mesh reconstruction: Total Variation Bound
Nikolaos Sfakianakis
We consider 3-point numerical schemes for scalar Conservation Laws, that are oscillatory either to their dispersive or anti-diffusive nature. Oscillations are responsible for the i…