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Elfverson, Daniel
Publications (10 of 11) Show all publications
Elfverson, D., Larson, M. G. & Målqvist, A. (2017). Multiscale methods for problems with complex geometry. Computer Methods in Applied Mechanics and Engineering, 321, 103-123
Open this publication in new window or tab >>Multiscale methods for problems with complex geometry
2017 (English)In: Computer Methods in Applied Mechanics and Engineering, ISSN 0045-7825, E-ISSN 1879-2138, Vol. 321, p. 103-123Article in journal (Refereed) Published
National Category
Computational Mathematics
Identifiers
urn:nbn:se:uu:diva-262266 (URN)10.1016/j.cma.2017.03.023 (DOI)000402461100006 ()
Available from: 2017-03-31 Created: 2015-09-11 Last updated: 2018-06-16Bibliographically approved
Elfverson, D., Hellman, F. & Målqvist, A. (2016). A multilevel Monte Carlo method for computing failure probabilities. SIAM/ASA Journal on Uncertainty Quantification, 4, 312-330
Open this publication in new window or tab >>A multilevel Monte Carlo method for computing failure probabilities
2016 (English)In: SIAM/ASA Journal on Uncertainty Quantification, ISSN 1560-7526, E-ISSN 2166-2525, Vol. 4, p. 312-330Article in journal (Refereed) Published
National Category
Computational Mathematics
Identifiers
urn:nbn:se:uu:diva-262259 (URN)10.1137/140984294 (DOI)000407996700014 ()
Available from: 2016-04-05 Created: 2015-09-11 Last updated: 2018-06-16Bibliographically approved
Elfverson, D. (2015). A discontinuous Galerkin multiscale method for convection–diffusion problems. Computing Research Repository (1509.03523)
Open this publication in new window or tab >>A discontinuous Galerkin multiscale method for convection–diffusion problems
2015 (English)In: Computing Research Repository, no 1509.03523Article in journal (Other academic) Submitted
National Category
Computational Mathematics
Identifiers
urn:nbn:se:uu:diva-262261 (URN)
Available from: 2015-09-11 Created: 2015-09-11 Last updated: 2015-10-12Bibliographically approved
Elfverson, D. (2015). Multiscale Methods and Uncertainty Quantification. (Doctoral dissertation). Uppsala: Acta Universitatis Upsaliensis
Open this publication in new window or tab >>Multiscale Methods and Uncertainty Quantification
2015 (English)Doctoral thesis, comprehensive summary (Other academic)
Abstract [en]

In this thesis we consider two great challenges in computer simulations of partial differential equations: multiscale data, varying over multiple scales in space and time, and data uncertainty, due to lack of or inexact measurements.

We develop a multiscale method based on a coarse scale correction, using localized fine scale computations. We prove that the error in the solution produced by the multiscale method decays independently of the fine scale variation in the data or the computational domain. We consider the following aspects of multiscale methods: continuous and discontinuous underlying numerical methods, adaptivity, convection-diffusion problems, Petrov-Galerkin formulation, and complex geometries.

For uncertainty quantification problems we consider the estimation of p-quantiles and failure probability. We use spatial a posteriori error estimates to develop and improve variance reduction techniques for Monte Carlo methods. We improve standard Monte Carlo methods for computing p-quantiles and multilevel Monte Carlo methods for computing failure probability.

Place, publisher, year, edition, pages
Uppsala: Acta Universitatis Upsaliensis, 2015. p. 32
Series
Digital Comprehensive Summaries of Uppsala Dissertations from the Faculty of Science and Technology, ISSN 1651-6214 ; 1287
Keywords
multiscale methods, finite element method, discontinuous Galerkin, Petrov-Galerkin, a priori, a posteriori, complex geometry, uncertainty quantification, multilevel Monte Carlo, failure probability
National Category
Computational Mathematics
Research subject
Scientific Computing with specialization in Numerical Analysis
Identifiers
urn:nbn:se:uu:diva-262354 (URN)978-91-554-9336-3 (ISBN)
Public defence
2015-10-30, Room 2446, Polacksbacken, Lägerhyddsvägen 2, Uppsala, 10:15 (English)
Opponent
Supervisors
Available from: 2015-10-08 Created: 2015-09-14 Last updated: 2015-10-12Bibliographically approved
Elfverson, D., Ginting, V. & Henning, P. (2015). On multiscale methods in Petrov–Galerkin formulation. Numerische Mathematik, 131, 643-682
Open this publication in new window or tab >>On multiscale methods in Petrov–Galerkin formulation
2015 (English)In: Numerische Mathematik, ISSN 0029-599X, E-ISSN 0945-3245, Vol. 131, p. 643-682Article in journal (Refereed) Published
National Category
Computational Mathematics
Identifiers
urn:nbn:se:uu:diva-242930 (URN)10.1007/s00211-015-0703-z (DOI)000365081600002 ()
Available from: 2015-01-11 Created: 2015-02-03 Last updated: 2017-12-05Bibliographically approved
Elfverson, D., Estep, D. J., Hellman, F. & Målqvist, A. (2014). Uncertainty quantification for approximate p-quantiles for physical models with stochastic inputs. SIAM/ASA Journal on Uncertainty Quantification, 2, 826-850
Open this publication in new window or tab >>Uncertainty quantification for approximate p-quantiles for physical models with stochastic inputs
2014 (English)In: SIAM/ASA Journal on Uncertainty Quantification, ISSN 1560-7526, E-ISSN 2166-2525, Vol. 2, p. 826-850Article in journal (Refereed) Published
National Category
Computational Mathematics
Identifiers
urn:nbn:se:uu:diva-242908 (URN)10.1137/140967039 (DOI)000421346900036 ()
Available from: 2014-12-23 Created: 2015-02-02 Last updated: 2018-06-16Bibliographically approved
Elfverson, D., Georgoulis, E. H. & Målqvist, A. (2013). An adaptive discontinuous Galerkin multiscale method for elliptic problems. Multiscale Modeling & simulation, 11, 747-765
Open this publication in new window or tab >>An adaptive discontinuous Galerkin multiscale method for elliptic problems
2013 (English)In: Multiscale Modeling & simulation, ISSN 1540-3459, E-ISSN 1540-3467, Vol. 11, p. 747-765Article in journal (Refereed) Published
National Category
Computational Mathematics
Identifiers
urn:nbn:se:uu:diva-200254 (URN)10.1137/120863162 (DOI)000325006000003 ()
Available from: 2013-08-01 Created: 2013-05-23 Last updated: 2017-12-06Bibliographically approved
Elfverson, D., Georgoulis, E. H., Målqvist, A. & Peterseim, D. (2013). Convergence of a discontinuous Galerkin multiscale method. SIAM Journal on Numerical Analysis, 51, 3351-3372
Open this publication in new window or tab >>Convergence of a discontinuous Galerkin multiscale method
2013 (English)In: SIAM Journal on Numerical Analysis, ISSN 0036-1429, E-ISSN 1095-7170, Vol. 51, p. 3351-3372Article in journal (Refereed) Published
National Category
Computational Mathematics
Identifiers
urn:nbn:se:uu:diva-200256 (URN)10.1137/120900113 (DOI)000328903500017 ()
Available from: 2013-12-11 Created: 2013-05-23 Last updated: 2017-12-06Bibliographically approved
Elfverson, D. & Målqvist, A. (2013). Discontinuous Galerkin multiscale methods for convection dominated problems.
Open this publication in new window or tab >>Discontinuous Galerkin multiscale methods for convection dominated problems
2013 (English)Report (Other academic)
Series
Technical report / Department of Information Technology, Uppsala University, ISSN 1404-3203 ; 2013-011
National Category
Computational Mathematics
Identifiers
urn:nbn:se:uu:diva-200257 (URN)
Available from: 2013-05-23 Created: 2013-05-23 Last updated: 2013-05-23Bibliographically approved
Elfverson, D. (2013). On discontinuous Galerkin multiscale methods. (Licentiate dissertation). Uppsala University
Open this publication in new window or tab >>On discontinuous Galerkin multiscale methods
2013 (English)Licentiate thesis, comprehensive summary (Other academic)
Abstract [en]

In this thesis a new multiscale method, the discontinuous Galerkin multiscale method, is proposed. The method uses localized fine scale computations to correct a global coarse scale equation and thereby takes the fine scale features into account. We show a priori error bounds for convection dominated diffusion-convection-reaction problems with variable coefficients. We also present a posteriori error bound in the case of no convection or reaction and present an adaptive algorithm which tunes the method parameters automatically. We also present extensive numerical experiments which verify our analytical findings.

Place, publisher, year, edition, pages
Uppsala University, 2013
Series
Information technology licentiate theses: Licentiate theses from the Department of Information Technology, ISSN 1404-5117 ; 2013-003
National Category
Computational Mathematics
Research subject
Scientific Computing with specialization in Numerical Analysis
Identifiers
urn:nbn:se:uu:diva-200260 (URN)
Supervisors
Available from: 2013-06-04 Created: 2013-05-23 Last updated: 2017-08-31Bibliographically approved
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