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Publications Submitted 28.A discontinuous Galerkin multiscale method for first order hyperbolic equations (Submitted) with Mats G. Larson and Robert Söderlund 27.An adaptive discontinuous Galerkin multiscale method for elliptic problems (Submitted) with Daniel Elfverson and Emmanuil Georgoulis 26.A variational multiscale method for Poissons equation on mixed form (Submitted) with Mats G.Larson and Robert Söderlund 25.Localization of elliptic multiscale problems (Submitted) with Daniel Peterseim 24.A priori error analysis of a multiscale method (Submitted) 2012 23.Nonparametric density estimation for randomly perturbed elliptic problems III: Convergence, complexity, and generalizations, J. Appl. Math. Comp. 38 (2012) 367-387 with Donald Estep and Michael J. Holst (link) 2011 22.Multiscale methods for elliptic problems, SIAM Multi. Model. Simul. 9 (2011) 1064-1086 (link) 21.A posteriori error estimates for mixed finite element approximations of parabolic problems, Numer. Math. 118 (2011) 33-48 with Mats G. Larson (link) 2010 20.Convergence analysis of finite element approximations of the Joule heating problem in three spatial dimensions, BIT 50 (2010) 781-795 with Michael J. Holst, Mats G. Larson, and Robert Söderlund (link) 19.Density estimation of multi-phase flow with multiscale and randomly perturbed data, Adv. Water Res. 33 (2010) 1130-1141 with Michael Presho and Victor Ginting (link) 18.Numerical Mathematics and Advanced Applications, Proceedings of ENUMATH 2009, the 8th European Conference on Numerical Mathematics and Advanced Applications, Uppsala, Sweden, Springer Verlag, 2010, (ed.) together with Gunilla Kreiss, Per Lötstedt, and Maya Neytcheva (link) 17.A novel method for solving multiscale elliptic problems with randomly perturbed data, SIAM Multi. Model. Simul. 8 (2010) 977-996 with Victor Ginting and Michael Presho (link) 2009 16.Adaptive variational multiscale methods, Oberwolfach reports 29 (2009) 1627-1629 (link) 15.Nonparametric density estimation for randomly perturbed elliptic problems II: applications and adaptive modeling, Int. J. Numer. Methods Engrg. 80 (2009) 846–867, with Donald Estep and Simon Tavener (link) 14.A mixed adaptive variational multiscale method with applications in oil reservoir simulation, Math. Models Methods Appl. Sci. 19 (2009) 1017-1042, with Mats G. Larson (link) 13.Nonparametric density estimation for randomly perturbed elliptic problems I: computational method, a posteriori analysis, and adaptive error control, SIAM J. Sci. Comp., 31 (2009) 2935-2959 with Donald Estep and Simon Tavener (link) 12.Adaptive variational multiscale method of convection-diffusion problems, Comm. Num. Methods Engrg. 25 (2009) 65-79, with Mats G. Larson (link) 2008 11.Adaptive variational multiscale methods, Proc. of 21st Nordic seminar on computational mechanics, 2008, Trondheim, Norway, with Mats G. Larson (pdf) 10.A posteriori error estimates for mixed finite element approximations of elliptic problems, Numer. Math. volume 108 number 3 (2008) 487-500, with Mats G. Larson (link) 2007 9.Numerical analysis and adaptive computation for solutions of elliptic problems with randomly perturbed coefficients, Proc. Appl. Math. Mech. 7, 1140401-1140402 (2007), with D. Estep and S. Tavener (link) 8.Goal oriented adaptivity for coupled flow and transport problems with applications in oil reservoir simulation, Comput. Methods Appl. Mech. Eng. 196 (2007) 3546-3561, with Mats G. Larson (link) 7.Adaptive variational multiscale methods based on a posteriori error estimation: Energy norm estimates for elliptic problems, Comput. Methods Appl. Mech. Engrg. 196 (2007) 2313–2324, with Mats G. Larson (link) 2006 6.A symmetric mixed adaptive variational multiscale method, Proceedings of XVI International Conference on Computational Methods in Water Resources, 2006, Copenhagen, with Mats G. Larson (link) 2005 5.Adaptive variational multiscale methods for elliptic problems, Proceedings of the third M.I.T. conference on Computational Fluid and Solid Mechanics, 2005, Cambridge, MA, USA, with Mats G. Larson (pdf) 4.Adaptive variational multiscale methods based on a posteriori error estimation: Duality techniques for elliptic problems, Lecture Notes in Computational Science and Engineering, B. Engquist, P. Lötstedt, O. Runborg (eds.) Vol. 44, 181-193, 2005. with Mats G. Larson 3.Adaptive variational multiscale methods (PhD thesis) 2005 2004 2. Adaptive variational multiscale methods based on a posteriori error estimation, Proceedings of ECCOMAS 2004 conference, Jyväskylä, Finland, with Mats G. Larson (link) 1.On adaptive finite element methods based on a posteriori error estimates (Lic. thesis) 2004 2001 0.Adaptive finite element methods for eigenvalue problems with applications in quantum physics (MSc. dissertation), 2001 Presentations 2011 Seminar, Humboldt University, Berlin, Germany, 2011-10-19, On convergence of a multiscale method Enumath 2011 conference, Leicester, UK, 2011-09-08, A posteriori error estimates for mixed finite element approximations of elliptic and parabolic problmes ICIAM 2011 conference, Vancouver, Canada, 2011-07-18, On convergence of multiscale methods Workshop, SIMULA Research Laboratory, Oslo, Norway, 2011-06-17, Multiscale methods for elliptic and hyperbolic problems Presentation at the PhD defence of Carl Joachim Berdal Haga, SIMULA Research Laboratory, Oslo, Norway, 2011-06-16, Numerical methods in poroelasticity KoF 2011 evaluation, Uppsala University, Uppsala, Sweden, 2011-05-10, Uncertainty quantification for multiscale problems 2010 Docent (Habilitation) lecture, Uppsala University, Uppsala, Sweden, 2010-12-01, Finita elementmetoder för multiskal- och multifysikproblem (in swedish) China-Norway-Sweden workshop on computational mathematics, University of Bergen, Bergen, Norway, 2010-06-10, Error estimation and adaptivity for multiscale methods 2009 Analaysis & applied mathematics seminar, University of Wyoming, Laramie, WY, USA, 2009-10-13, Multiscale methods for elliptic problems Enumath 09 conference, Uppsala, Sweden, 2009-06-29, Adaptive variational multiscale methods Workshop on Computational Multiscale Methods, Oberwolfach, Germany, 2009-06-17, Adaptive variational multiscale methods SIAM conference on computational science and engineering, Miami, Florida, USA, 2009-03-02, Adaptive variational multiscale methods with applications in oil reservoir simulation 2008 Applied Mathematics Seminar, University of Leicester, UK, 2008-11-13, Adaptive variational multiscale methods DqF workshop, Royal Institute of Technology, Stockholm, Sweden, 2008-10-20, Nonparametric density estimation for elliptic problems with random perturbations European finite element fair, Göteborg, Sweden, 2008-05-30, Finite element methods for the Joule heating problem in three spatial dimensions 2007 NA seminar, Royal Institute of Technology, Stockholm, Sweden, 2007-10-17, Adaptive variational multiscale methods TDB seminar, Uppsala University, Uppsala, Sweden, 2007-10-10, Adaptive variational multiscale methods 6th International Congress on Industrial and Applied Mathematics, ETH, Zurich, Switzerland, 2007-07-18, Adaptive variational multiscale methods for convection-diffusion problems 6th International Congress on Industrial and Applied Mathematics, ETH, Zurich, Switzerland, 2007-07-16, Numerical analysis and adaptive computation for solutions of elliptic problems with randomly perturbed coefficients Research group meeting, Ft Collins, Colorado, USA, 2007-06-04, Existence of weak solutions to the coupled nonlinear Joule heating problem SIAM conference on computational science and engineering, Costa Mesa, California, USA, 2007-02-19, Numerical analysis and adaptive computation for solutions of elliptic problems with randomly perturbed coefficients 2006 CAM seminar, Göteborg, Sweden, 2006-12-20, Error estimation and adaptive computation for elliptic problems with randomly perturbed coefficients CAM seminar at UCSD, La Jolla, California, USA, 2006-11-07, Error estimation and adaptive computation for elliptic problems with randomly perturbed coefficients Presentation at UCSD, La Jolla, California, USA, 2006-10-24, Error estimation and adaptive computation for linear partial differential equations with randomly perturbed data 2nd multi-all workshop, Ft Collins, Colorado, USA, 2006-09-28, Sensitivity analysis for solutions to partial differential equations with randomly perturbed data Computational methods in water resources XVI, Copenhagen, Denmark, 2006-06-22, A mixed adaptive variational multiscale method CAM seminar, Göteborg, Sweden, 2006-05-31, Sensitivity analysis for linear functionals of solutions to partial differential equations CAM seminar, Göteborg, Sweden, 2006-01-05, Adaptive variational multiscale methods for convection-diffusion problems 2005 Presentation at Sandia National Laboratories, Albuquerque, New Mexico, USA, 2005-12-06, Adaptive variational multiscale methods Presentation at UCSD, La Jolla, California, USA, 2005-12-01, Adaptive variational multiscale methods Informal seminars held at CSU, Ft. Collins, Colorado, USA, 2005-10-17, 2005-10-24, and 2005-12-13, Adaptive variational multiscale methods Doctoral thesis defence, Göteborg, Sweden, 2005-09-30, Adaptive variational multiscale methods Third M.I.T. conference on computational fluid and solid mechanics, Cambridge, Massachusetts, USA, 2005-06-14, A new mixed multiscale method for oil reservoir simulation Presentation at SIMULA, Oslo, Norway, 2005-05-12, A new mixed multiscale method for oil reservoir simulation Presentation at SINTEF, Oslo, Norway, 2005-05-12, A new mixed multiscale method for oil reservoir simulation Presentation at SINTEF, Oslo, Norway, 2005-05-03, A posteriori error analysis, based on duality, in oil reservoir simulation: A model problem 2004 Multiscale Modeling, and Applications in Fluid Flow and Material Science, Oslo, Norway, 2004-10-18, Error analysis of the adaptive variational multiscale method ECCOMAS 2004 mini-symposium, Jyväskylä, Finland, 2004-07-27, Adaptive variational multiscale methods based on a posteriori error estimation UNICC mini-symposium, Göteborg, Sweden, 2004-05-27, Adaptive variational multiscale methods based a posteriori error estimation Licentiate thesis presentation, Göteborg, Sweden, 2004-05-07, On adaptive finite element methods based on a posteriori error estimates CAM seminar, Göteborg, Sweden, 2004-02-05, Adaptive variational multiscale method: basic a posteriori error estimation framework Multiscale Methods in Science and Engineering, Uppsala, Sweden, 2004-01-27, Adaptive variational multiscale method: basic a posteriori error estimation framework 2001 CAM seminar, Göteborg, Sweden, 2001-10-04, Adaptive finite element methods for eigenvalue problems with applications in quantum physics Visits/Conferences 2011 Grading committee at the PhD defence of Henrik Holst, Royal Institute of Technology, Stockholm, Sweden, 9th dec Visiting Humboldt University, Berlin, Germany, 18th oct-20th oct ENUMATH 11 conference, Leicester, UK, 5th sep-9th sep Grading committee at the PhD defence of Murtazo Nazarov, Royal Institute of Technology, Stockholm, Sweden, 1st sep ICIAM 11 conference, Vancouver, Canada, 18th jul-22th jul 1st opponent at the PhD defence of Carl Joachim Berdal Haga, SIMULA Research Laboratory, Oslo, Norway, 16-17th jun Visiting Umeå University, Umeå, Sweden, 4th may-5th may Grading committee at the PhD defence of David Heintz, Chalmers University of Technology, Göteborg, Sweden, 3rd mar Grading committee at the PhD defence of Karin Kraft, Chalmers University of Technology, Göteborg, Sweden, 25th feb 2010 China-Norway-Sweden workshop on Computational Mathematics, Bergen, Norway, 7th jun-11th jun Visiting University of Wyoming, Laramie, Wyoming, USA, 29th may Visiting Colorado State University, Ft. Collins, Colorado, USA, 20th apr-1st jun 2009 Visiting Colorado State University, Ft. Collins, Colorado, USA, 14th oct-18th oct Visiting University of Wyoming, Laramie, Wyoming, USA, 12th oct-13th oct Visiting Umeå University, Umeå, Sweden, 7th sep-8th sep ENUMATH 09 conference, Uppsala, Sweden, 29th jun-3rd jul Workshop on Computational Multiscale Methods, Oberwolfach, Germany, 14th jun-20th jun SIAM conference on computational science and engineering, Miami, Florida, USA, 2nd mar-6th mar 2008 Visiting University of Leicester, Leicester, UK, 12th nov-16th nov DqF workshop, Royal Institute of Technoloy, Stockholm, Sweden, 20th oct-21st oct European Finite Element Fair, Chalmers University of Technology, Göteborg, Sweden, 30th may-31st may 2007 Discussion leader at the Licentiate defence of Fredrik Bengzon, Umeå University, Umeå, Sweden, 4th dec-5th dec Visiting Colorado State University, Ft. Collins, Colorado, USA, 21st nov-24th nov Visiting University of California San Diego, La Jolla, California, USA, 19th nov-21st nov ICIAM 07, ETH, Zurich, Switzerland, 16th jul-20th jul Visiting Colorado State University, Ft. Collins, Colorado, USA, 31st may-6th jun SIAM conference on computational science and engineering, Costa Mesa, California, USA, 19th feb-23 feb 2006 Visiting Chalmers University of Technology, Göteborg, Sweden, 20th dec-9th jan (2006-2007) 2nd Multi-all workshop, Colorado State University, Ft. Collins, Colorado, USA, 26th sep-30th sep Computational methods in water resources XVI, Copenhagen, Denmark, 19th jun-22nd jun Visiting Chalmers University of Technology, Göteborg, Sweden, 20th may-18th jun AtC Coupling Methods Workshop at Sandia National Labs, Albuquerque, New Mexico, USA, 20th mar-22th mar Visiting Chalmers University of Technology, Göteborg, Sweden, 2nd jan-9th jan 2005 Working meeting at Sandia National Laboratories, Albuquerque, New Mexico, USA, 5th dec-7th dec Visiting University of California San Diego, La Jolla, California, USA, 30th nov-3th dec Multi-all workshop, Colorado State University, Ft. Collins, Colorado, USA, 5th sep-8th sep Third M.I.T. Conference on Comp. Fluid and Solid Mech., Cambridge, Massachusetts, USA, 14th jun-17th jun Visiting SINTEF Applied Mathematics, Oslo, Norway, 2nd may-12th may 2004 Workshop on Multiscale Modeling, University of Oslo, Norway, 18th oct-20th oct 4th ECCOMAS conference, University of Jyväskylä, Finland, 24th jul-28th jul Conference on Multiscale Methods in Science and Engineering, University of Uppsala, Sweden, 26th jan-28th jan 2002 X-th Summer School in Numerical Analysis, University of Durham, UK, 8th jul-12th jul 2001 Computing Laboratory, Oxford University, UK, jan-jun