My research focuses on numerical methods for nonlinear partial differential equations. In particular, I have been working on convergence proofs for hyperbolic conservation laws and (degenerate) parabolic equations with applications in fluid mechanics, magnetohydrodynamics and liquid crystals. Current projects include work on resonant hyperbolic systems that occur in the modeling of oil reservoirs, conservation laws with non-local flux functions that model traffic flow, and numerical methods to solve models for plant growth.

### Publications

G. M. Coclite, J. Ridder, N. H. Risebro. A convergent finite difference scheme for the

variational heat equation. *Zeitschrift für Angewandte Mathematik und Physik*, 68:123, 2017. doi:10.1007/s00033-017-0871-z

G. M. Coclite, J. Ridder, N. H. Risebro. A convergent finite difference scheme for the OstrovskyHunter equation. *BIT Numerical Mathematics*, 57(1):93–122, 2017. doi:10.1007/s10543-016-0625-x

J. Ridder. Convergence of a finite difference scheme for two-dimensional incompressible magnetohydrodynamics. *SIAM Journal on Numerical Analysis*, 54(6):3550–3576, 2016. doi:10.1137/15M1042024

P. Aursand, G. Napoli, J. Ridder. On the dynamics of the weak Fréedericksz transition for

nematic liquid crystals. *Communications in Computational Physics*, 20(5):1359–1380, 2016. doi:10.4208/cicp.190615.090516a

P. Aursand, J. Ridder. The influence of inertia on the dynamics of the director for a nematic liquid crystal coupled with an electric field. Communications in Computational Physics, 18(1):147–166, 2015. doi:10.4208/cicp.220414.231214a

My PhD thesis: Finite difference methods for nonlinear evolution equations: Convergence proofs and applications to liquid crystals. Advisors: N. H. Risebro, G. M. Coclite. Download pdf

### Preprints

J. Ridder, A. M. Ruf. A convergent finite difference scheme for the Ostrovsky–Hunter equation with Dirichlet boundary conditions, 2018. arXiv:1805.07255

J. Ridder, W. Shen. Traveling Waves for Nonlocal Models of Traffic Flow, 2018. arXiv:1808.03734

### Education

2017: PhD in Mathematics, University of Oslo (Norway)

2013: MSc ETH Applied Mathematics, ETH Zürich (Switzerland)

2011: BSc Technomathematik (industrial mathematics), TU Berlin (Germany)

2009/10: exchange year at Zhejiang University (China)