@article {24801,
	title = {Parameter-robust discretization and preconditioning of Biot{\textquoteright}s consolidation model},
	journal = {SIAM Journal of Scientific Computing},
	volume = {39},
	year = {2017},
	pages = {1-24},
	publisher = {SIAM},
	doi = {10.1137/15M1029473},
	author = {Lee, Jeonghun and Mardal, Kent-Andre and Winther, Ragnar}
}
@inbook {24042,
	title = {Computational Partial Differential Equations},
	booktitle = {Encyclopedia of Applied and Computational Mathematics},
	volume = {1},
	year = {2015},
	month = {09/2015},
	pages = {271-278},
	publisher = {Springer-Verlag},
	organization = {Springer-Verlag},
	edition = {1},
	address = {Berlin, Heidelberg},
	isbn = {978-3-540-70528-4},
	author = {Tveito, Aslak and Hans Petter {Langtangen} and Winther, Ragnar},
	editor = {Engquist, Bj{\"o}rn}
}
@article {Simula.simula.836,
	title = {A Uniformly Stable Fortin Operator for the Taylor-Hood Element},
	journal = {Numerische Mathematik},
	volume = {123},
	number = {3},
	year = {2013},
	pages = {537-551},
	doi = {dx.doi.org/10.1007/s00211-012-0492-6},
	author = {Mardal, Kent-Andre and Schoberl, Joachim and Winther, Ragnar}
}
@techreport {Simula.simula.2086,
	title = {A Uniform Inf-Sup Condition With Applications to Preconditioning},
	year = {2012},
	publisher = {Simula},
	author = {Mardal, Kent-Andre and Schoberl, Joachim and Winther, Ragnar}
}
@inbook {Simula.sc.862,
	title = {Construction of Preconditioners by Mapping Properties for Systems of Partial Differential Equations},
	booktitle = {Efficient preconditioning methods for elliptic partial differential equations},
	year = {2011},
	pages = {65-84},
	publisher = {Bentham Science Publishers},
	organization = {Bentham Science Publishers},
	chapter = {4},
	isbn = {978-1-60805-291-2},
	author = {Mardal, Kent-Andre and Winther, Ragnar},
	editor = {Axelsson, Owe and Karatson, Janos}
}
@article {Simula.SC.570,
	title = {Preconditioning Discretizations of Systems of Partial Differential Equations},
	journal = {Numerical Linear Algebra with Applications},
	volume = {18},
	number = {1},
	year = {2011},
	note = {Listed in annual report 2010. Appeared online April 2010.},
	pages = {1-40},
	abstract = {This survey paper is based on three talks given by the second author at the London Mathematical Society Durham Symposium on Computational Linear Algebra for Partial Differential Equations in the summer of 2008. The main focus will be on an abstract approach to the construction of preconditioners for symmetric linear systems in a Hilbert space setting. Typical examples that are covered by this theory are systems of partial differential equations which correspond to saddle point problems. We will argue that the mapping properties of the coefficient operators suggest that block diagonal preconditioners are natural choices for these systems. To illustrate our approach a number of examples will be considered. In particular, parameter-dependent systems arising in areas like incompressible flow, linear elasticity, and optimal control theory will be studied. The paper contains analysis of several models which have previously been discussed in the literature. However, here each example is discussed with reference to a more unified abstract approach.},
	doi = {10.1002/nla.716},
	author = {Mardal, Kent-Andre and Winther, Ragnar}
}
@article {Simula.SC.566,
	title = {Mixed Finite Element Methods for Viscoelasticity With Weak Symmetry},
	journal = {Mathematical Models and Methods in Applied Sciences (M3AS)},
	volume = {20},
	number = {6},
	year = {2010},
	pages = {955-985},
	abstract = {Small deformations of a viscoelastic body are considered through the linear Maxwell and Kelvin-Voigt models in the quasi-static equilibrium. A robust mixed finite element method, enforcing the symmetry of the stress tensor weakly, is proposed for these equations on simplicial tessellations in two and three dimensions. A priori error estimates are derived and numerical experiments presented. The approach can be applied to general models for linear viscoelasticity and thus offers a unifed framework.},
	doi = {10.1142/S0218202510004490},
	author = {Marie E. {Rognes} and Winther, Ragnar}
}
@book {Simula.SC.266,
	title = {Introduction to Partial Differential Equations; a Computational Approach},
	volume = {29},
	year = {2009},
	note = {392 pages},
	publisher = {Springer},
	organization = {Springer},
	edition = {second},
	address = {Berlin Heidelberg},
	abstract = {This is the softcover reprint of a popular book teaching the basic analytical and computational methods of partial differential equations. Standard topics such as separation of variables, Fourier analysis, maximum principles, and energy estimates are included. Prerequisites for this text are the very basics of calculus, linear algebra and ordinary differential equations. Numerical methods are included in the book to show the significance of computations in partial differential equations, and to illustrate the strong interaction between mathematical theory and numerical methods. Great care has been taken throughout the book to seek a sound balance between the analytical and numerical techniques. The authors present the material at an easy pace with exercises and projects ranging from the straightforward to the challenging. The text would be suitable for advanced undergraduate and graduate courses in mathematics and engineering, and it develops basic tools of computational science.},
	isbn = {978-3-540-88704-1},
	author = {Tveito, Aslak and Winther, Ragnar}
}
@article {Simula.SC.21,
	title = {Unified Finite Element Discretizations of Coupled Darcy-Stokes Flow},
	journal = {Numerical Methods for Partial Differential Equations},
	volume = {25},
	year = {2009},
	pages = {311-326},
	publisher = {Wiley Periodicals},
	author = {Trygve K. {Karper} and Mardal, Kent-Andre and Winther, Ragnar}
}
@article {Mardal.2006.1,
	title = {An Observation on Korn{\textquoteright}s Inequality for Nonconforming Finite Element Methods},
	journal = {Math. Comp.},
	volume = {75},
	number = {253},
	year = {2006},
	pages = {1-6},
	author = {Mardal, Kent-Andre and Winther, Ragnar}
}
@article {SC.4.Mardal.2004,
	title = {Uniform Preconditioners for the Time Dependent Stokes Problem},
	journal = {Numerische Mathematik},
	volume = {98},
	number = {2},
	year = {2004},
	pages = {305-327},
	author = {Mardal, Kent-Andre and Winther, Ragnar}
}
@book {SC.1.Tveito.2002,
	title = {Einf{\"u}hrung in Die Theorie Der Partiellen Differentialgleichungen; Ein Numerischer Zugang},
	year = {2002},
	note = {430 pages},
	publisher = {Springer},
	organization = {Springer},
	address = {Berlin Heidelberg},
	author = {Tveito, Aslak and Winther, Ragnar}
}
@article {SC.4.Langtangen.2002.b,
	title = {Numerical Methods for Incompressible Viscous Flow},
	journal = {Advances in Water Resources},
	volume = {25},
	number = {8},
	year = {2002},
	pages = {1125-1146},
	author = {Hans Petter {Langtangen} and Mardal, Kent-Andre and Winther, Ragnar}
}
@article {SC.4.Lyche.2002,
	title = {Preconditioned Iterative Methods for Scattered Data Interpolation},
	journal = {Advances in Computational Mathematics},
	volume = {17},
	year = {2002},
	pages = {237-256},
	author = {Lyche, T. and Nilssen, Trygve Kastberg and Winther, Ragnar}
}
@article {SC.4.Mardal.2002,
	title = {A Robust Finite Element Method for Darcy-Stokes Flow},
	journal = {SIAM Journal on Numerical Analysis},
	volume = {40},
	year = {2002},
	pages = {1605-1631},
	author = {Mardal, Kent-Andre and Tai, Xue-Cheng and Winther, Ragnar}
}
@article {SC.4.Nilssen.2001,
	title = {A Robust Nonconforming H2-Element},
	journal = {Mathematics of Computation},
	volume = {70},
	year = {2001},
	pages = {489-505},
	author = {Nilssen, Trygve Kastberg and Tai, Xue-Cheng and Winther, Ragnar}
}
@misc {SC.8.Nilssen.2000.b,
	title = {Preconditioned Iterative Methods for Scattered Data Interpolation},
	howpublished = {Talk at the Mathematical Methods for Curves and Surfaces, Oslo, Norway},
	year = {2000},
	author = {Nilssen, Trygve Kastberg and Winther, Ragnar}
}
@article {SC.4.Shen.1999,
	title = {On the Zero Relaxation Limit for a System Modeling the Motions of a Viscoelastic Solid},
	journal = {Siam J. of Math. Anal.},
	volume = {30},
	number = {5},
	year = {1999},
	pages = {1115-1135,},
	author = {Shen, W. and Tveito, Aslak and Winther, Ragnar}
}
@inproceedings {SC.5.Shen.1998,
	title = {Rate of Convergence for the Zero Relaxation Limit},
	journal = {Proceedings of the seventh international conference on hyperbolic problems},
	year = {1998},
	type = {1},
	address = {Z{\"u}rich,},
	author = {Shen, W. and Tveito, Aslak and Winther, Ragnar}
}
@article {SC.4.Schroll.1997,
	title = {An L^1-Error Bound for a Finite Difference Scheme Applied to a Stiff System of Conservation Laws},
	journal = {SIAM J. Numer. Anal.},
	volume = {34},
	number = {3},
	year = {1997},
	pages = {1152-1166,},
	author = {H. J. {Schroll} and Tveito, Aslak and Winther, Ragnar}
}
@article {SC.4.Tveito.1997,
	title = {On the Rate of Convergence to Equilibrium for a System of Conservation Laws Including a Relaxation Term},
	journal = {SIAM Journal on Mathematical Analysis},
	volume = {28},
	number = {1},
	year = {1997},
	pages = {136-161,},
	author = {Tveito, Aslak and Winther, Ragnar}
}
@article {SC.4.Langseth.1996,
	title = {On the Convergence of Operator Splitting Applied to Conservation Laws With Source Terms},
	journal = {SIAM J. Numer. Anal.},
	volume = {33},
	year = {1996},
	pages = {843-863,},
	author = {J. O. {Langseth} and Tveito, Aslak and Winther, Ragnar}
}
@article {SC.4.Shen.1996,
	title = {A System of Conservation Laws Including a Stiff Relaxation Term; the 2D Case},
	journal = {BIT},
	volume = {36},
	number = {4},
	year = {1996},
	pages = {786-813,},
	author = {Shen, W. and Tveito, Aslak and Winther, Ragnar}
}
@article {SC.4.Tveito.1995,
	title = {The Solution of Nonstrictly Hyperbolic Systems of Conservation Laws May Be Hard to Compute},
	journal = {SIAM J. Sci. Comput.},
	volume = {16},
	year = {1995},
	pages = {320-329,},
	author = {Tveito, Aslak and Winther, Ragnar}
}
@inproceedings {SC.5.Tveito.1994,
	title = {A System of Conservation Laws With a Relaxation Term},
	journal = {Proceedings of the fifth international conference on hyperbolic problems},
	year = {1994},
	pages = {786-813},
	type = {1},
	address = {Stony Brook, New York,},
	author = {Tveito, Aslak and Winther, Ragnar}
}
@techreport {SC.7.Bruaset.1993,
	title = {Efficient Solution of Linear Equations Arising in a Nonlinear Economic Model},
	number = {STF33 A93021},
	year = {1993},
	publisher = {SINTEF},
	author = {Are Magnus {Bruaset} and Winther, Ragnar}
}
@article {SC.4.Tveito.1993,
	title = {An Error Estimate for a Finite Difference Scheme Approximating a Hyperbolic System of Conservation Laws},
	journal = {SIAM J. Numer. Anal.},
	volume = {30},
	year = {1993},
	pages = {401-424,},
	author = {Tveito, Aslak and Winther, Ragnar}
}
@inproceedings {SC.5.Tveito.1992,
	title = {Hyperbolic Conservation Laws, Finite Difference Schemes and Error Estimates},
	journal = {Proceedings of the fourth international conference on hyperbolic problems},
	year = {1992},
	pages = {1-8},
	type = {1},
	address = {Taormina, Italy,},
	author = {Tveito, Aslak and Winther, Ragnar and L{\o}vereide, T.}
}
@article {SC.4.Langtangen.1992.a,
	title = {Instability of Buckley-Leverett Flow in a Heterogeneous Medium},
	journal = {Transport in Porous Media},
	volume = {9},
	year = {1992},
	pages = {165-18,},
	author = {Hans Petter {Langtangen} and Tveito, Aslak and Winther, Ragnar}
}
@article {SC.4.Dahl.1992,
	title = {Multicomponent Chromatography in a Two-Phase Environment},
	journal = {SIAM J. Appl. Math.},
	volume = {52},
	year = {1992},
	pages = {65-104,},
	author = {Dahl, O. and Johansen, T. and Tveito, Aslak and Winther, Ragnar}
}
@article {SC.4.Tveito.1991,
	title = {Existence, Uniqueness and Continuous Dependence for a System of Hyberbolic Conservation Laws Modeling Polymer Flooding},
	journal = {Siam J. of Math. Anal.},
	volume = {22},
	year = {1991},
	pages = {905-933,},
	author = {Tveito, Aslak and Winther, Ragnar}
}
@article {SC.4.Tveito.1990,
	title = {Convergence of a Non-Conservative Finite Difference Scheme for a System of Hyperbolic Conservation Laws},
	journal = {J. of Diff. and Integ. Eq.},
	volume = {3},
	year = {1990},
	pages = {979-1000,},
	author = {Tveito, Aslak and Winther, Ragnar}
}
@article {SC.4.Bruaset.1990,
	title = {On the Stability of Relaxed Incomplete LU Factorizations},
	journal = {Math. Comp.},
	volume = {54},
	year = {1990},
	pages = {701-719,},
	author = {Are Magnus {Bruaset} and Tveito, Aslak and Winther, Ragnar}
}
@article {SC.4.Johansen.1989,
	title = {A Riemann Solver for a Two-Phase Multicomponent Process},
	journal = {SIAM Journal on Scientific and Statistical Computing},
	volume = {10,},
	year = {1989},
	author = {Johansen, T. and Tveito, Aslak and Winther, Ragnar}
}
