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