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Landsberg C.,Institute For Wissenschaftliches Rechnen | Voigt A.,Institute For Wissenschaftliches Rechnen
Computing and Visualization in Science | Year: 2010

We develop a multigrid finite element approach to solve PDE's on surfaces. The multigrid approach involves the same weights for restriction and prolongation as in the case of planar domains. Combined with the concept of parametric finite elements the approach thus allows to reuse code initially developed to solve problems on planar domains to solve the corresponding problem on surfaces. The method is tested on a non-linear reaction-diffusion system on stationary and evolving surfaces, with the normal velocity of the evolving surface depending on the reaction-diffusion system. As a reference model the Schnakenberg system is used, offering non-linearity and algebraic simplicity on one hand, and quantitative reference data on the other hand. © Springer-Verlag 2010.

Aland S.,Institute For Wissenschaftliches Rechnen | Voigt A.,Institute For Wissenschaftliches Rechnen
International Journal for Numerical Methods in Fluids | Year: 2012

Diffuse interface models for incompressible two-phase flow with large density ratios are tested on benchmark configurations for a two-dimensional bubble rising in liquid columns. The benchmark quantities circularity, center of mass, and mean rise velocity are compared with reference solutions from Hysing et al. © 2011 John Wiley & Sons, Ltd.

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