Ragnar Winther

Bilde av Ragnar Winther
English version of this page
Telefon +47 22855935
Mobiltelefon +47 48153210
Rom 1211
Brukernavn
Besøksadresse Moltke Moes vei 35 Niels Henrik Abels hus 0851 Oslo
Postadresse Postboks 1053 Blindern 0316 Oslo

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. 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:

Emneord: Matematikk, Partielle differensiallikninger

Publikasjoner

  • Lee, Jeonghun & Winther, Ragnar (2018). Local coderivatives and approximation of Hodge Laplace problems. Mathematics of Computation. ISSN 0025-5718. 87(314), s. 2709–2735. doi: 10.1090/mcom/3315. Fulltekst i vitenarkiv
  • 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(3), s. 377–396. doi: 10.1515/cmam-2017-0016. Fulltekst i vitenarkiv
  • 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. Fulltekst i vitenarkiv
  • 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. Fulltekst i vitenarkiv
  • 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. Fulltekst i vitenarkiv
  • 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. Fulltekst i vitenarkiv
  • 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. Fulltekst i vitenarkiv
  • 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.
  • Winther, Ragnar & Mardal, Kent-Andre (2011). Construction of preconditioners by mapping properties for systems of partial differential equations. I Axelsson, Owe & Karatson, Janos (Red.), Efficient Preconditioned Solution Methods for Elliptic Partial Differential Equations. Bentham eBooks. ISSN 978-1-60805-291-2. s. 65–83.
  • 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.
  • Arnold, DN; Falk, RS & Winther, Ragnar (2010). FINITE ELEMENT EXTERIOR CALCULUS FROM HODGE THEORY TO NUMERICAL STABILITY. Bulletin of the American Mathematical Society. ISSN 0273-0979. 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.
  • 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.
  • 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.
  • 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.
  • 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.
  • Christiansen, Snorre H & Winther, Ragnar (2008). Smoothed projections in finite element exterior calculus. Mathematics of Computation. ISSN 0025-5718. 77.
  • 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.
  • 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.
  • 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; 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.
  • Tai, Xue-Cheng & Winther, Ragnar (2006). A discrete de Rham complex with enhanced smoothness. Calcolo. ISSN 0008-0624. 43(4), s. 287–306.
  • 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.
  • 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). Robust convergence of multi point flux approximation on rough grids. Numerische Mathematik. ISSN 0029-599X. 104, s. 317–337.
  • 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.
  • 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 & Mardal, Kent-Andre (2004). Uniform preconditioners for the time dependent Stokes problem. Numerische Mathematik. ISSN 0029-599X. 98, s. 305–327.
  • Winther, Ragnar (2003). Nonconforming mixed methods for elasticity. Mathematical Models and Methods in Applied Sciences. ISSN 0218-2025. 13, s. 295–307.
  • Winther, Ragnar (2003). Mixed finite elements for elasticity in the stress-displacement formulation. Contemporary Mathematics. ISSN 0271-4132. 329, s. 33–42.
  • 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.
  • Arnold, Douglas N. & Winther, Ragnar (2002). Mixed finite elements for elasticity. Numerische Mathematik. ISSN 0029-599X. 92, s. 401–419.
  • 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 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.
  • 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.
  • 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, 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(5), 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.
  • 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.
  • 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 (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.

Se alle arbeider i Cristin

  • Tveito, Aslak & Winther, Ragnar (2009). Introduction to Partial Differential Equations; A Computational Approach. Springer. ISBN 978-3-540-88704-1. 392 s.
  • Winther, Ragnar & Tveito, Aslak (2002). Einfuhrung in die Theorie der partiellen Differentialgleichungen;Ein numericher Zugang. Springer.
  • Tveito, Aslak & Winther, Ragnar (2002). Einfuhrung in partielle differentalgleichungen, Ein numerischer zugang. Springer. ISBN 3-540-42404-0. 392 s.
  • Tveito, Aslak & Winther, Ragnar (1998). Introduction to Partial Differential Equations; A computational Approach. Springer. 29. 400 s.

Se alle arbeider i Cristin

  • Hu, Kaibo & Winther, Ragnar (2017). Well-Conditioned Frames for Finite Element Methods.
  • Winther, Ragnar (2014). Local bounded cochain projections and the bubble transform.
  • Winther, Ragnar (2014). Local bounded cochain projections and the bubble transform.
  • Winther, Ragnar (2012). Five Lectures on Finite Element Exterior Calculus.
  • Winther, Ragnar (2012). Uniform preconditioners and the Taylor-Hood method.
  • 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 (2011). Finite element exterior calculus - a link between topology and numerical analysis.
  • Winther, Ragnar (2011). Bounded cochain projections, why and how.
  • Winther, Ragnar (2011). Bounded cochain projections and finite elementexterior calculus.
  • Winther, Ragnar (2010). Introduction to finite element exterior calculus.
  • 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 (2009). Preconditioning discretizations of systems of partial differential equations.
  • Winther, Ragnar (2008). Smoothed projections in finite element exterior calculus.
  • Winther, Ragnar (2008). Mixed finite elements for linear elasticity and viscoelasticity.
  • Winther, Ragnar (2008). Finite element discretizations of the elasticity complex.
  • Winther, Ragnar (2008). Preconditioning saddle point problems arising from discretizations of partial differential equations (3 lectures).
  • Winther, Ragnar (2008). Finite element exterior calculus - a link between algebraic topology and numerical analysis.
  • Winther, Ragnar (2006). Finite element exterior calculus and applications.
  • Winther, Ragnar (2005). Exact sequences and mixed finite elements for elasticity.
  • Winther, Ragnar (2005). Mixed finite elements for elasticity, a constructive approach.
  • Winther, Ragnar (2005). A discrete de Rham complex with enhanced smoothness.
  • Winther, Ragnar & Ellingsrud, Geir (2004). Matematiske muligheter. Dagbladet. ISSN 0805-3766.
  • Winther, Ragnar (2004). Matematiske muligheter.
  • Winther, Ragnar (2004). From the de Rham sequence to mixed finite elements for elasticity.
  • Winther, Ragnar (2004). Robust preconditioners for mixed systems.
  • Winther, Ragnar (2004). Preconditioning saddle point systems.
  • Winther, Ragnar (2004). On the construction of mixed finite elements for elasticity.
  • Mardal, Kent-Andre; Winther, Ragnar & Langtangen, Hans Petter (2001). An optimal iterative approach to the time-dependent Stokes problem.
  • Winther, Ragnar (2001). Robust finite elements for mixed systems.
  • Winther, Ragnar (2001). Robust preconditioners for mixed systems.
  • Winther, Ragnar (2001). A robust finite element method for Darcy-Stokes flow.
  • Langtangen, Hans Petter; Mardal, Kent-Andre & Winther, Ragnar (2001). An efficient parallel iterative approach to the time-dependent Stokes problem.
  • 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.
  • Muntingh, Agnar Georg Peder; Piene, Ragni & Winther, Ragnar (2011). Topics in Polynomial Interpolation Theory. Unipub forlag. ISSN 1501-7710. 1056(1056).
  • Halvorsen, Tore Gunnar; Christiansen, Snorre H & Winther, Ragnar (2009). Structure preserving discretizations of wave equations from theoretical physics. Unipub AS.
  • Christiansen, Snorre H & Winther, Ragnar (2006). Smoothed projections in finite element exterior calculus. Department of Mathematics.
  • Winther, Ragnar & Mardal, Kent-Andre (2004). An observation on Korn's inequality for nonconforming finite element methods. Centre of Mathematics for Applications, Universitetet i Oslo.
  • Christiansen, Snorre H & Winther, Ragnar (2004). On constraint preservation in numerical simulations of Yang-Mills equations. Matematisk Institutt, Universitetet i Oslo.
  • Winther, Ragnar & Østby, Ivar (2003). Stability of a model of human granulopoiesis using continuous maturation. Institutt for Informatikk, UiO.
  • Mardal, Kent-Andre & Winther, Ragnar (2002). Uniform preconditioners for the time dependent Stokes problem.
  • 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.
  • Arnold, Douglas N. & Winther, Ragnar (2002). Mixed finite elements for elasticity in the stress-displacement formulation.
  • Mardal, Kent-Andre; Tai, Xue-Cheng & Winther, Ragnar (2001). A robust finite element method for Darcy-Stokes flow.
  • Arnold, Douglas N. & Winther, Ragnar (2001). Mixed finite elements for elasticity.

Se alle arbeider i Cristin

Publisert 13. nov. 2010 14:47 - Sist endret 23. nov. 2021 15:16

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