Ragnar Winther

Image of Ragnar Winther
Norwegian version of this page
Phone +47-22855935
Room 1009
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Visiting address Ullevål stadion Sognsveien 77 B 0855 OSLO
Postal address Postboks 1053 Blindern 0316 OSLO
Other affiliations Department of Mathematics

Presentation

I was director of the Centre of Mathematics for Applications CMA since the start in 2003 to 2013. CMA was one of the first thirteen Norwegian centres of excellence supported by the Research Council of Norway. From 2004 to 2010 I was serving as chairman of the board of the Niels Henrik Abel Memorial Fund.

My research interests are partial differential equations and numerical analysis. In particular, lately I have focused on the development of compatible discretization methods , in particular on finite element exterior calculus.

Editorial boards

  • SIAM Journal on Scientific Computing (1998--2004), see here.
  • Numerical Analysis and Modeling, see here.
  • BIT, see here.

Recent preprints:

Tags: Mathematics, Partial Differential Equations, Centre of Mathematics for Applications - CMA, China, USA

Publications

  • Bærland, Trygve; Lee, Jeonghun J.; Mardal, Kent-Andre & Winther, Ragnar (2017). Weakly Imposed Symmetry and Robust Preconditioners for Biot’s Consolidation Model. Computational Methods in Applied Mathematics.  ISSN 1609-4840.  17(17) . doi: https://doi.org/10.1515/cmam-2017-0016
  • Lee, Jeonghun; Mardal, Kent-Andre & Winther, Ragnar (2017). Parameter-robust discretization and preconditioning of Biot's consolidation model. SIAM Journal on Scientific Computing.  ISSN 1064-8275.  39(1), s A1- A24 . doi: 10.1137/15M1029473 Full text in Research Archive.
  • Falk, Richard S. & Winther, Ragnar (2015). Double complexes and local cochain projections. Numerical Methods for Partial Differential Equations.  ISSN 0749-159X.  31(2), s 541- 551 . doi: 10.1002/num.21922 Full text in Research Archive.
  • Falk, Richard S. & Winther, Ragnar (2015). The Bubble Transform: A New Tool for Analysis of Finite Element Methods. Foundations of Computational Mathematics.  ISSN 1615-3375.  16(1), s 297- 328 . doi: 10.1007/s10208-015-9252-1 Full text in Research Archive.
  • Arnold, Douglas N.; Awanou, Gerard & Winther, Ragnar (2014). Nonconforming tetrahedral mixed finite elements for elasticity. Mathematical Models and Methods in Applied Sciences.  ISSN 0218-2025.  24(4), s 783- 796 . doi: 10.1142/S021820251350067X Full text in Research Archive.
  • Falk, Richard S. & Winther, Ragnar (2014). Local bounded cochain projections. Mathematics of Computation.  ISSN 0025-5718.  83(290), s 2631- 2656 . doi: 10.1090/S0025-5718-2014-02827-5 Full text in Research Archive.
  • Christiansen, Snorre H & Winther, Ragnar (2013). On variational eigenvalue approximation of semidefinite operators. IMA Journal of Numerical Analysis.  ISSN 0272-4979.  33(1), s 164- 189 . doi: 10.1093/imanum/drs002
  • Mardal, Kent-Andre; Schoberl, Joachim & Winther, Ragnar (2013). A uniformly stable Fortin operator for the Taylor-Hood element. Numerische Mathematik.  ISSN 0029-599X.  123(3), s 537- 551 . doi: 10.1007/s00211-012-0492-6
  • Mardal, Kent-Andre & Winther, Ragnar (2011). Preconditioning discretizations of systems of partial differential equations. Numerical Linear Algebra with Applications.  ISSN 1070-5325.  18(1), s 1- 40 . doi: 10.1002/nla.716
  • Winther, Ragnar & Mardal, Kent-Andre (2011). Construction of preconditioners by mapping properties for systems of partial differential equations, In Owe Axelsson & Janos Karatson (ed.),  Efficient Preconditioned Solution Methods for Elliptic Partial Differential Equations.  Bentham eBooks.  ISBN 978-1-60805-291-2.  Chapter 4.  s 65 - 83
  • Arnold, DN; Falk, RS & Winther, Ragnar (2010). FINITE ELEMENT EXTERIOR CALCULUS FROM HODGE THEORY TO NUMERICAL STABILITY. Bulletin of the American Mathematical Society.  ISSN 1088-9485.  47(2), s 281- 354
  • Winther, Ragnar & Rognes, Marie Elisabeth (2010). Mixed finite element methods for linear viscoelasticity using weak symmetry. Mathematical Models and Methods in Applied Sciences.  ISSN 0218-2025.  20(6), s 955- 985 . doi: 10.1142/S0218202510004490
  • Arnold, Douglas N.; Falk, Richard S. & Winther, Ragnar (2009). Geometric decompositions and local bases for spaces of finite element differential forms. Computer Methods in Applied Mechanics and Engineering.  ISSN 0045-7825.  198(21-26), s 1660- 1672 . doi: 10.1016/j.cma.2008.12.017
  • Hu, Qiya; Tai, Xue-Cheng & Winther, Ragnar (2009). A saddle point approach to the computation of harmonic maps. SIAM Journal on Numerical Analysis.  ISSN 0036-1429.  47(2), s 1500- 1523 . doi: 10.1137/060675575
  • Karper, Trygve Klovning; Mardal, Kent-Andre & Winther, Ragnar (2009). Unified Finite Element Discretizations of Coupled Darcy-Stokes Flow. Numerical Methods for Partial Differential Equations.  ISSN 0749-159X.  25(2), s 311- 326 . doi: 10.1002/num.20349
  • Arnold, DN; Awanou, G & Winther, Ragnar (2008). Finite elements for symmetric tensors in three dimensions. Mathematics of Computation.  ISSN 0025-5718.  77, s 1229- 1251
  • Christiansen, Snorre H & Winther, Ragnar (2008). Smoothed projections in finite element exterior calculus. Mathematics of Computation.  ISSN 0025-5718.  77
  • Karper, Trygve Klovning; Mardal, Kent-Andre & Winther, Ragnar (2008). Unified finite element discretizations of coupled Darcy-Stokes flow. Numerical Methods for Partial Differential Equations.  ISSN 0749-159X.  25(2), s 311- 326
  • Arnold, DN; Falk, RS & Winther, Ragnar (2007). Mixed finite element methods for linear elasticity with weakly imposed symmetry. Mathematics of Computation.  ISSN 0025-5718.  76, s 1699- 1723
  • Christiansen, Snorre Harald & Winther, Ragnar (2006). On constraint preservation in numerical simulations of Yang-Mills equations. SIAM Journal on Scientific Computing.  ISSN 1064-8275.  28
  • Klausen, Runhild Aae & Winther, Ragnar (2006). Convergence of multipoint flux approximations on quadrilateral grids. Numerical Methods for Partial Differential Equations.  ISSN 0749-159X.  22, s 1438- 1454
  • Klausen, Runhild Aae & Winther, Ragnar (2006). Robust convergence of multi point flux approximation on rough grids. Numerische Mathematik.  ISSN 0029-599X.  104, s 317- 337
  • Tai, Xue-Cheng & Winther, Ragnar (2006). A discrete de Rham complex with enhanced smoothness. Calcolo (Testo stampato).  ISSN 0008-0624.  43(4), s 287- 306
  • Winther, Ragnar; Arnold, Douglas N. & Falk, Richard S. (2006). Differential complexes and stability of finite element methods. I: The de Rham complex. IMA Volumes in Mathematics and its Applications.  ISSN 0940-6573.  142, s 23- 46
  • Winther, Ragnar; Arnold, Douglas N. & Falk, Richard S. (2006). Differential complexes and stability of finite element methods. II: The elasticity complex. IMA Volumes in Mathematics and its Applications.  ISSN 0940-6573.  142, s 47- 68
  • Winther, Ragnar; Arnold, Douglas N. & Falk, Richard S. (2006). Finite element exterior calculus. Acta Numerica.  ISSN 0962-4929.  15, s 1- 155
  • Winther, Ragnar & Mardal, Kent-Andre (2006). An observation on Korn's inequality for nonconforming finite element methods. Mathematics of Computation.  ISSN 0025-5718.  75(253), s 1- 6
  • Winther, Ragnar & Mardal, Kent-Andre (2004). Uniform preconditioners for the time dependent Stokes problem. Numerische Mathematik.  ISSN 0029-599X.  98, s 305- 327
  • Østby, Ivar & Winther, Ragnar (2004). Stability of a model of human granulopoiesis using continuous maturation. Journal of Mathematical Biology.  ISSN 0303-6812.  49, s 501- 536
  • Winther, Ragnar (2003). Mixed finite elements for elasticity in the stress-displacement formulation. Contemporary Mathematics.  ISSN 0271-4132.  329, s 33- 42
  • Winther, Ragnar (2003). Nonconforming mixed methods for elasticity. Mathematical Models and Methods in Applied Sciences.  ISSN 0218-2025.  13, s 295- 307
  • Arnold, Douglas N. & Winther, Ragnar (2002). Mixed finite elements for elasticity. Numerische Mathematik.  ISSN 0029-599X.  92, s 401- 419
  • Langtangen, Hans Petter; Mardal, Kent-Andre & Winther, Ragnar (2002). Numerical methods for incompressible viscous flow. Advances in Water Resources.  ISSN 0309-1708.  25, s 1125- 1146
  • Lyche, Tom Johan; Nilssen, Trygve Kastberg & Winther, Ragnar (2002). Preconditioned Iterative Methods for Scattered Data Interpolation. Advances in Computational Mathematics.  ISSN 1019-7168.  17, s 237- 256
  • Mardal, Kent-Andre; Tai, Xue-Cheng & Winther, Ragnar (2002). A robust finite element method for Darcy-Stokes flow. SIAM Journal on Numerical Analysis.  ISSN 0036-1429.  40, s 1605- 1631
  • Lyche, Tom; Nilssen, Trygve Kastberg & Winther, Ragnar (2001). Preconditioned iterative methods for Scattered Data Interpolation. Advances in Computational Mathematics.  ISSN 1019-7168.  70, s 489- 505 Show summary
  • Nilssen, Trygve Kastberg; Tai, Xue-Cheng & Winther, Ragnar (2001). A robust nonconforming H2-element. Mathematics of Computation.  ISSN 0025-5718.  70, s 489- 505
  • Arnold, Douglas N.; Falk, Richard S. & Winther, Ragnar (2000). Multigrid in H(div) and H(curl). Numerische Mathematik.  ISSN 0029-599X.  85, s 197- 217
  • Shen, Wen; Tveito, Aslak & Winther, Ragnar (1999). On the zero relaxation limit for a system modeling the motions of a viscoelastic solid. SIAM Journal on Mathematical Analysis.  ISSN 0036-1410.  30(5), s 1115- 1135
  • Shen, Wen; Tveito, Aslak & Winther, Ragnar (1999). On the zero relaxation limit for a system modeling the motions of a viscoelastic solid. SIAM Journal on Mathematical Analysis.  ISSN 0036-1410.  30, s 1115- 1135
  • Rusten, Torgeir; Vassilevski, Panayot S. & Winther, Ragnar (1998). Domain embedding preconditioners for mixed systems. Numerical Linear Algebra with Applications.  ISSN 1070-5325.  5, s 321- 345
  • Schroll, H. J.; Tveito, Aslak & Winther, Ragnar (1997). An L^1-error bound for finite difference scheme applied to a stiff system of conservation laws. SIAM Journal on Numerical Analysis.  ISSN 0036-1429.  34(3), s 1152- 1166
  • Langseth, J. O.; Tveito, Aslak & Winther, Ragnar (1996). On the convergence of operator splitting applied to conservation laws with source terms. SIAM Journal on Numerical Analysis.  ISSN 0036-1429.  33, s 843- 863
  • Shen, Wen; Tveito, Aslak & Winther, Ragnar (1996). A system of conservation laws including a stiff relaxation term; the 2D case. BIT Numerical Mathematics.  ISSN 0006-3835.  36:4, s 786- 813
  • Tveito, Aslak & Winther, Ragnar (1996). On the rate of convergence to equilibrium for a system of conservation laws including a relaxation term. SIAM Journal on Mathematical Analysis.  ISSN 0036-1410.  28:1, s 136- 161
  • Tveito, Aslak & Winther, Ragnar (1995). The solutions of nonstrictly hyperbolic systems of conservation laws may be hard to compute. SIAM Journal on Scientific Computing.  ISSN 1064-8275.  16, s 320- 329
  • Bruaset, Are Magnus & Winther, Ragnar (1994). A numerical study of optimized sparse preconditioners. BIT Numerical Mathematics.  ISSN 0006-3835.  34, s 177- 204
  • Tveito, Aslak & Winther, Ragnar (1993). An error estimate for a finite difference scheme approximating a hyperbolic system of conservation laws. SIAM Journal on Numerical Analysis.  ISSN 0036-1429.  30, s 401- 424
  • Dahl, Olav; Johansen, T.; Tveito, Aslak & Winther, Ragnar (1992). Multicomponent chromatography in a two-phase environment. SIAM Journal on Applied Mathematics.  ISSN 0036-1399.  52, s 65- 104 . doi: 10.1137/0152005

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  • Tveito, Aslak & Winther, Ragnar (ed.) (2009). Introduction to Partial Differential Equations; A Computational Approach. Springer.  ISBN 978-3-540-88704-1.  392 s.
  • Tveito, Aslak & Winther, Ragnar (2002). Einfuhrung in partielle differentalgleichungen, Ein numerischer zugang. Springer.  ISBN 3-540-42404-0.  392 s.
  • Winther, Ragnar & Tveito, Aslak (2002). Einfuhrung in die Theorie der partiellen Differentialgleichungen;Ein numericher Zugang. Springer.
  • Tveito, Aslak & Winther, Ragnar (1998). Introduction to Partial Differential Equations; A computational Approach. Springer.  400 s.

View all works in Cristin

  • Winther, Ragnar (2014). Local bounded cochain projections and the bubble transform.
  • Winther, Ragnar (2014). Local bounded cochain projections and the bubble transform.
  • Berre, Inga; Dahle, Helge K.; Karlsen, Kenneth Hvistendahl; Nordbotten, Jan Martin; Tai, Xue-Cheng & Winther, Ragnar (2012). Magne Espedal Memorial Issue. International Journal of Numerical Analysis & Modeling.  ISSN 1705-5105.  9(3), s I- II
  • Winther, Ragnar (2012). Five Lectures on Finite Element Exterior Calculus.
  • Winther, Ragnar (2012). Uniform preconditioners and the Taylor-Hood method.
  • Muntingh, Agnar Georg Peder; Piene, Ragni & Winther, Ragnar (2011). Topics in Polynomial Interpolation Theory. Series of dissertations submitted to the Faculty of Mathematics and Natural Sciences, University of Oslo.. 1056.
  • Winther, Ragnar (2011). Bounded cochain projections and finite elementexterior calculus.
  • Winther, Ragnar (2011). Bounded cochain projections, why and how.
  • Winther, Ragnar (2011). Finite element exterior calculus - a link between topology and numerical analysis.
  • Winther, Ragnar (2010). Cochain projections in finite element exterior calculus.
  • Winther, Ragnar (2010). Finite element exterior calculus - from Hodge theory to numerical stability.
  • Winther, Ragnar (2010). Introduction to finite element exterior calculus.
  • Halvorsen, Tore Gunnar; Christiansen, Snorre H & Winther, Ragnar (2009). Structure preserving discretizations of wave equations from theoretical physics.
  • Winther, Ragnar (2009). Preconditioning discretizations of systems of partial differential equations.
  • Winther, Ragnar (2008). Finite element discretizations of the elasticity complex.
  • Winther, Ragnar (2008). Finite element exterior calculus - a link between algebraic topology and numerical analysis.
  • Winther, Ragnar (2008). Mixed finite elements for linear elasticity and viscoelasticity.
  • Winther, Ragnar (2008). Preconditioning saddle point problems arising from discretizations of partial differential equations (3 lectures).
  • Winther, Ragnar (2008). Smoothed projections in finite element exterior calculus.
  • Christiansen, Snorre H & Winther, Ragnar (2006). Smoothed projections in finite element exterior calculus.
  • Winther, Ragnar (2006). Finite element exterior calculus and applications.
  • Winther, Ragnar (2005). A discrete de Rham complex with enhanced smoothness.
  • Winther, Ragnar (2005). Exact sequences and mixed finite elements for elasticity.
  • Winther, Ragnar (2005). Mixed finite elements for elasticity, a constructive approach.
  • Christiansen, Snorre H & Winther, Ragnar (2004). On constraint preservation in numerical simulations of Yang-Mills equations.
  • Winther, Ragnar (2004). From the de Rham sequence to mixed finite elements for elasticity.
  • Winther, Ragnar (2004). Matematiske muligheter.
  • Winther, Ragnar (2004). On the construction of mixed finite elements for elasticity.
  • Winther, Ragnar (2004). Preconditioning saddle point systems.
  • Winther, Ragnar (2004). Robust preconditioners for mixed systems.
  • Winther, Ragnar & Ellingsrud, Geir (2004). Matematiske muligheter. Dagbladet.  ISSN 0805-3766.
  • Winther, Ragnar & Mardal, Kent-Andre (2004). An observation on Korn's inequality for nonconforming finite element methods.
  • Winther, Ragnar & Østby, Ivar (2003). Stability of a model of human granulopoiesis using continuous maturation.
  • Arnold, Douglas N. & Winther, Ragnar (2002). Mixed finite elements for elasticity in the stress-displacement formulation.
  • Arnold, Douglas N. & Winther, Ragnar (2002). Nonconforming mixed elements for elasticity.
  • Langtangen, Hans Petter; Mardal, Kent-Andre & Winther, Ragnar (2002). Numerical methods for incompressible viscous flow.
  • Mardal, Kent-Andre & Winther, Ragnar (2002). Uniform preconditioners for the time dependent Stokes problem.
  • Arnold, Douglas N. & Winther, Ragnar (2001). Mixed finite elements for elasticity.
  • Langtangen, Hans Petter; Mardal, Kent-Andre & Winther, Ragnar (2001). An efficient parallel iterative approach to the time-dependent Stokes problem.
  • Mardal, Kent-Andre; Tai, Xue-Cheng & Winther, Ragnar (2001). A robust finite element method for Darcy-Stokes flow.
  • Mardal, Kent-Andre; Winther, Ragnar & Langtangen, Hans Petter (2001). An optimal iterative approach to the time-dependent Stokes problem.
  • Winther, Ragnar (2001). A robust finite element method for Darcy-Stokes flow.
  • Winther, Ragnar (2001). Robust finite elements for mixed systems.
  • Winther, Ragnar (2001). Robust preconditioners for mixed systems.
  • Winther, Ragnar (1999). A nonconforming finite element method for a fourth order singular perturbation problem.
  • Winther, Ragnar (1999). A robust nonconforming H2-element.
  • Shen, Wen; Tveito, Aslak & Winther, Ragnar (1998). Rate of convergence for the zero relaxation limit.

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Published Nov. 30, 2010 11:20 PM - Last modified Jan. 20, 2017 9:58 AM