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- Andreas Prohl, Markus Schmuck
- Numerische Mathematik
- 2009

We propose and analyse two convergent fully discrete schemes to solve the incompressible Navier-Stokes-Nernst-Planck-Poisson system. The first scheme converges to weak solutions satisfying an energy and an entropy dissipation law. The second scheme uses Chorin’s projection method to obtain an efficient approximation that converges to strong solutions at… (More)

- M Schmuck, M Pradas, S Kalliadasis, G A Pavliotis
- Physical review letters
- 2013

We present a new methodology for studying non-Hamiltonian nonlinear systems based on an information theoretical extension of a renormalization group technique using a modified maximum entropy principle. We obtain a rigorous dimensionally reduced description for such systems. The neglected degrees of freedom by this reduction are replaced by a systematically… (More)

- Markus Schmuck, Grigorios A. Pavliotis, Serafim Kalliadasis
- Appl. Math. Lett.
- 2014

We study phase field equations in perforated domains for arbitrary free energies. These equations have found numerous applications in a wide spectrum of both science and engineering problems with homogeneous environments. Here, we focus on strongly heterogeneous materials with perforations such as porous media. To the best of our knowledge, we provide the… (More)

- Markus Schmuck, Martin Z. Bazant
- SIAM Journal of Applied Mathematics
- 2015

Effective Poisson-Nernst-Planck (PNP) equations are derived for macroscopic ion transport in charged porous media. Homogenization analysis is performed for a two-component periodic composite consisting of a dilute electrolyte continuum (described by standard PNP equations) and a continuous dielectric matrix, which is impermeable to the ions and carries a… (More)

- Markus Schmuck
- Appl. Math. Lett.
- 2015

- POROUS MEDIA, MARKUS SCHMUCK, MARTIN Z. BAZANT
- 2015

Effective Poisson–Nernst–Planck (PNP) equations are derived for ion transport in charged porous media under forced convection (periodic flow in the frame of the mean velocity) by an asymptotic multiscale expansion with drift. The homogenized equations provide a modeling framework for engineering while also addressing fundamental questions about… (More)

- Markus Schmuck, Serafim Kalliadasis
- SIAM Journal of Applied Mathematics
- 2017

- Antonios Ververis, Markus Schmuck
- J. Comput. Physics
- 2017

- M. Schmuck
- 2015

Consider the generalized Kuramoto–Sivashinsky (gKS) equation. It is a model prototype for a wide variety of physical systems, from flame-front propagation, and more general front propagation in reaction– diffusion systems, to interface motion of viscous film flows. Our aim is to develop a systematic and rigorous low-dimensional representation of the gKS… (More)