Carnegie Mellon University
Mellon College of Science  ›  Mathematical Sciences  ›  People  ›  Faculty  ›  Franziska Weber

Franziska Weber

Associate Professor

Address:
8206 Wean Hall
Department of Mathematical Sciences
Carnegie Mellon University
5000 Forbes Avenue
Pittsburgh, PA 15213

P: 412-268-4732

Email

Website

Person's Name

Education

Ph.D., University of Oslo

Awards

  • NSF CAREER Award

Research

I am interested in the analysis and numerical approximation of nonlinear partial differential equations emerging in fluid dynamics, multi-phase flows, complex fluids and mathematical biology. I work on the development of efficient and convergent numerical methods for these phenomena.

Besides that, I have worked on uncertainty quantification using multilevel Monte Carlo methods for nonlinear evolution equations. More recently, I have become interested in problems related to turbulence and statistical descriptions of solutions of systems of conservation laws.

Select Publications

J. Bedrossian, M. Coti Zelati, S. Punshon-Smith, F. Weber. A sufficient condition for the Kolmogorov 4/5 law for stationary martingale solutions to the 3D Navier-Stokes equations, to appear in Communications in Mathematical Physics

K. Trivisa, F. Weber. Analysis and simulations on a model for the evolution of tumors under the influence of nutrient and drug application. SIAM J. Numer. Anal. 56 (2018), no. 1, 542–569.

U. Koley, N. H. Risebro, Ch. Schwab, F. Weber. Multilevel Monte Carlo for Random Degenerate Scalar Convection Diffusion Equation. J. Hyper. Differential Equations 14 (2017), no. 415.

F. Weber. Convergence rates of finite difference schemes for the linear advection and wave equation with rough coefficient. IMA Journal of Numerical Analysis. 37 (2017), no. 3, 1538-1634.

K. Trivisa, F. Weber. A convergent explicit finite difference scheme for a mechanical model for tumor growth. ESAIM: Mathematical Modelling and Numerical Analysis, 51 (2017), no. 1, 35-62.

N. H. Risebro, Ch. Schwab, F. Weber. Multilevel Monte Carlo front-tracking for random scalar conservation laws. BIT Numerical Mathematics 56 (2015), no. 1, pp. 263-292.

G. M. Coclite, S. Mishra, N. H. Risebro, F. Weber. Analysis and numerical approximation of Brinkman regularization of two-phase flows in porous media. Comput. Geosci. 18 (2014), no. 5, 637-659.

T. K. Karper, F. Weber. A new angular momentum method for computing wave maps into spheres. SIAM J. Numer. Anal. 52 (2014), no. 4, 2073-2091.