26 citations · 36 across the 15 of their papers we have counts for
17 papers
Global existence of weak solutions to a two-phase diffuse interface model of ferrofluids dynamics
Samuel Lanthaler, Franziska Weber
Ferrofluids are a class of materials that exhibit both fluid and magnetic properties. We consider a two-phase diffuse interface model for the dynamics of ferrofluids on a bounded d…
A Convergent Finite Element Scheme for the Q-Tensor Model of Liquid Crystals Subjected to an Electric Field
Max Hirsch, Franziska Weber
We study the Landau-de Gennes Q-tensor model of liquid crystals subjected to an electric field and develop a fully discrete numerical scheme for its solution. The scheme uses a con…
On the Convergence of an IEQ-based first-order Numerical Scheme for the Beris-Edwards System
Franziska Weber, Yukun Yue
We present a convergence analysis of an unconditionally energy-stable first-order semi-discrete numerical scheme designed for a hydrodynamic Q-tensor model, the so-called Beris-Edw…
A new reduced order model of linear parabolic PDEs
Noel Walkington, Franziska Weber, Yangwen Zhang
How to build an accurate reduced order model (ROM) for multidimensional time dependent partial differential equations (PDEs) is quite open. In this paper, we propose a new ROM for…
On the vanishing viscosity limit of statistical solutions of the incompressible Navier-Stokes equations
Ulrik Skre Fjordholm, Siddhartha Mishra, Franziska Weber
We study statistical solutions of the incompressible Navier-Stokes equation and their vanishing viscosity limit. We show that a formulation using correlation measures, which are pr…
Well-posedness of Bayesian inverse problems for hyperbolic conservation laws
Siddhartha Mishra, David Ochsner, Adrian M. Ruf +1
We study the well-posedness of the Bayesian inverse problem for scalar hyperbolic conservation laws where the statistical information about inputs such as the initial datum and (po…
On Bayesian data assimilation for PDEs with ill-posed forward problems
Samuel Lanthaler, Siddhartha Mishra, Franziska Weber
We study Bayesian data assimilation (filtering) for time-evolution PDEs, for which the underlying forward problem may be very unstable or ill-posed. Such PDEs, which include the Na…
A convergent numerical scheme for a model of liquid crystal dynamics subjected to an electric field
Franziska Weber
We present a convergent and constraint-preserving numerical discretization of a mathematical model for the dynamics of a liquid crystal subjected to an electric field. This model c…
Convergence analysis of a fully discrete energy-stable numerical scheme for the Q-tensor flow of liquid crystals
Varun M. Gudibanda, Franziska Weber, Yukun Yue
We present a fully discrete convergent finite difference scheme for the Q-tensor flow of liquid crystals based on the energy-stable semi-discrete scheme by Zhao, Yang, Gong, and Wa…
Statistical solutions of hyperbolic systems of conservation laws: numerical approximation
Ulrik Skre Fjordholm, Kjetil Lye, Siddhartha Mishra +1
Statistical solutions are time-parameterized probability measures on spaces of integrable functions, that have been proposed recently as a framework for global solutions and uncert…
Sufficient conditions for dual cascade flux laws in the stochastic 2d Navier-Stokes equations
Jacob Bedrossian, Michele Coti Zelati, Sam Punshon-Smith +1
We provide sufficient conditions for mathematically rigorous proofs of the third order universal laws capturing the energy flux to large scales and enstrophy flux to small scales f…
On the dynamics of ferrofluids: Global weak solutions to the Rosensweig system and rigorous convergence to equilibrium
Ricardo H. Nochetto, Konstantina Trivisa, Franziska Weber
This article establishes the global existence of weak solutions to a model proposed by Rosensweig (Rosensweig, Ferrohydrodynamics (1985)) for the dynamics of ferrofluids. The syste…
A sufficient condition for the Kolmogorov 4/5 law for stationary martingale solutions to the 3D Navier-Stokes equations
Jacob Bedrossian, Michele Coti Zelati, Samuel Punshon-Smith +1
We prove that statistically stationary martingale solutions of the 3D Navier-Stokes equations on subjected to white-in-time (colored-in-space) forcing satisfy the Ko…
Convergence rates of finite difference schemes for the linear advection and wave equation with rough coefficient
Franziska Weber
We prove convergence rates of explicit finite difference schemes for the linear advection and wave equation in one space dimension with Hölder continuous coefficient. The obtained…
Analysis and Simulation on a Model for the Evolution of Tumors under the Influence of Nutrient and Drug Application
Konstantina Trivisa, Franziska Weber
We investigate the evolution of tumor growth relying on a nonlinear model of partial differential equations which incorporates mechanical laws for tissue compression combined with…
A convergent explicit finite difference scheme for a mechanical model for tumor growth
Konstantina Trivisa, Franziska Weber
Mechanical models for tumor growth have been used extensively in recent years for the analysis of medical observations and for the prediction of cancer evolution based on imaging a…
A new angular momentum method for computing wave maps into spheres
Trygve Karper, Franziska Weber
In this paper, we present and analyze a new finite difference method for computing three dimensional wave maps into spheres. By introducing the angular momentum as an auxiliary var…