# Franziska Weber

## Assistant Professor

**Address:**

8206 Wean Hall

Department of Mathematical Sciences

Carnegie Mellon University

5000 Forbes Avenue

Pittsburgh, PA 15213

**P:** 412-268-4732

# Education

Ph.D., University of Oslo

# 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.