I am a PhD student in numerical analysis at the Centre for Interdisciplinary Mathematics (CIM) and Division of Scientific Computing. I am working on a research project on computer simulation of geologic carbon dioxide sequestration processes. My focus is on a few aspects of such a simulation. First, methods for uncertainty quantification of quantities achieved from such a simulation, e.g., capacity of a reservoir. Second, methods for multi-scale treatment of the multi-phase flow problem that arises when modeling the sequestration process.

My principal supervisor is Docent Axel Målqvist at Department of Mathematical Sciences, University of Gothenburg, and my two co-supervisors Prof. Auli Niemi and Docent Fritjof Fagerlund are at the Program for Air, Water and Landscape Sciences, Uppsala University.

# Research

### Publications

- F. Hellman and A. Målqvist,
*Contrast independent localization of multiscale problems*, submitted, arXiv - F. Hellman, P. Henning, and A. Målqvist,
*Multiscale mixed finite elements*, Discrete and Continuous Dynamical Systems - Series S (DCDS-S), 9(5), 2016, pp. 1269-1298, doi - F. Fagerlund, F. Hellman, A. Målqvist, and A. Niemi,
*Multilevel Monte Carlo methods for computing failure probability of porous media flow systems*, Advances in Water Resources, 94, 2016, pp. 498-509. - D. Elfverson, F. Hellman, and A. Målqvist,
*A multilevel Monte Carlo method for computing failure probabilities*, SIAM/ASA J. Uncertainty Quantification, 4(1), 2016, pp. 312-330, doi - D. Elfverson, D. J. Estep, F. Hellman, and A. Målqvist,
*Uncertainty quantification for approximate p-quantiles for physical models with stochastic inputs*, SIAM/ASA J. Uncertainty Quantification, 2(1), 2014, pp. 826-850, doi - H. Bar-Gera, F. Hellman, and M. Patriksson,
*Computational precision of traffic equilibria sensitivities in automatic network design and road pricing*, Transportation Research Part B: Methodological, 57, 2013, pp. 485-500, doi

### Presentations

- European Finite Element Fair 2016, Bonn, Germany, 2016-05-20, Fast decay of corrected basis functions
- SIAM UQ 16 conference, Lausanne, Switzerland, 2016-04-06, Multilevel Monte Carlo methods for computing failure probability
- Chemnitz FEM Symposium, Burgstädt, Germany, 2015-09-29, Mixed multiscale finite elements
- Licentiate seminar, Uppsala, Sweden, 2015-09-25, Multiscale and Multilevel Methods for Porous Media Flow Problems
- SIAM GS 15 conference, Stanford University, CA, US, 2015-07-01, Monte Carlo methods for failure probabilities - Using error bounds to reduce costs
- Seminar, INS, University of Bonn, Bonn, Germany, 2015-05-07, A multilevel Monte Carlo method for failure probabilities
- Numerical Analysis Seminar, Kungliga Tekniska högskolan (KTH), Sweden, 2014-10-30, A multilevel Monte Carlo method for failure probabilities
- Seminar, Centre for Interdisciplinary Mathematics, Uppsala University, Sweden, 2014-10-21, A mixed finite element multiscale method for Poisson's equation
- Oberseminar Angewandte Mathematik, University of Münster, Münster, Germany, 2014-09-04, A multilevel Monte Carlo method for failure probabilities
- SIAM UQ 14 conference, Savannah, GA, USA, 2014-03-31, Quantile bounds for numerical models with data uncertainty
- Seminar, Centre for Interdisciplinary Mathematics, Uppsala University, Sweden, 2013-05-14, Quantile estimation for numerical solution of stochastic PDEs

### Visits

- Attending SIAM UQ 16 conference, Lausanne, Switzerland, 5th Apr - 8th Apr 2016, presentation 2016-06-04 (see above)
- Attending Chemnitz FEM Symposium, Burgstädt, Germany, 28th Sep - 30th Sep 2015
- Attending SIAM GS 15 conference, Stanford University, CA, USA, 29th Jun - 2nd Jul 2015
- Visiting INS, University of Bonn, Bonn, Germany, 4th May - 8th May 2015
- Visiting SINTEF, Oslo, Norway, 8th Dec - 12th Dec 2014
- Attending International Conference on Numerical and Mathematical Modeling of Flow and Transport in Porous Media, Dubrovnik, Croatia, 29th Sep - 3rd Oct 2014, poster presentation 2014-09-30 (pdf)
- Visiting University of Münster, Münster, Germany, 3rd Sep - 5th Sep 2014, presentation 2014-09-04 (see above)
- Attending SIAM UQ 14 conference, Savannah, GA, USA, 31st Mar - 3rd Apr 2014, presentation 2014-03-31 (see above)
- Attending SIAM GS 13 conference, Padova, Italy, 17th Jun - 20th Jun 2013
- Visiting Colorado State University, Fort Collins, CO, USA, 1st Oct - 10th Oct 2012

### Co-authors and collaborators

Daniel Elfverson, Donald Estep, Fritjof Fagerlund, Patrick Henning, Axel Målqvist, Auli Niemi

# Teaching

- Scientific Computing I (W1B), Uppsala University, P4 2016
- Scientific Computing I (K1B), Uppsala University, P3 2016
- Scientific Computing I (K1A, X1A), Uppsala University, P3 2015
- Scientific Computing I (K1A), Uppsala University, P3 2014
- Scientific Computing I (F1AB), Uppsala University, P2 2013
- Scientific Computing I (F1AB), Uppsala University, P2 2012