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    Results of the third Marine Ice Sheet Model Intercomparison Project (MISMIP+)
    (Katlenburg-Lindau : Copernicus, 2020) Cornford, Stephen L.; Seroussi, Helene; Asay-Davis, Xylar S.; Gudmundsson, G. Hilmar; Arthern, Rob; Borstad, Chris; Christmann, Julia; dos Santos, Thiago Dias; Feldmann, Johannes; Goldberg, Daniel; Hoffman, Matthew J.; Humbert, Angelika; Kleiner, Thomas; Leguy, Gunter; Lipscomb, William H.; Merino, Nacho; Durand, Gaël; Morlighem, Mathieu; Pollard, David; Rückamp, Martin; Williams, C. Rosie; Yu, Hongju
    We present the result of the third Marine Ice Sheet Model Intercomparison Project, MISMIP+. MISMIP+ is intended to be a benchmark for ice-flow models which include fast sliding marine ice streams and floating ice shelves and in particular a treatment of viscous stress that is sufficient to model buttressing, where upstream ice flow is restrained by a downstream ice shelf. A set of idealized experiments first tests that models are able to maintain a steady state with the grounding line located on a retrograde slope due to buttressing and then explore scenarios where a reduction in that buttressing causes ice stream acceleration, thinning, and grounding line retreat. The majority of participating models passed the first test and then produced similar responses to the loss of buttressing. We find that the most important distinction between models in this particular type of simulation is in the treatment of sliding at the bed, with other distinctions - notably the difference between the simpler and more complete treatments of englacial stress but also the differences between numerical methods - taking a secondary role. © 2020 Wolters Kluwer Medknow Publications. All rights reserved.
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    Canonical sets of best L1-approximation
    (New York, NY : Hindawi, 2012) Dryanov, D.; Petrov, P.
    In mathematics, the term approximation usually means either interpolation on a point set or approximation with respect to a given distance. There is a concept, which joins the two approaches together, and this is the concept of characterization of the best approximants via interpolation. It turns out that for some large classes of functions the best approximants with respect to a certain distance can be constructed by interpolation on a point set that does not depend on the choice of the function to be approximated. Such point sets are called canonical sets of best approximation. The present paper summarizes results on canonical sets of best L1-approximation with emphasis on multivariate interpolation and best L1-approximation by blending functions. The best L1-approximants are characterized as transfinite interpolants on canonical sets. The notion of a Haar-Chebyshev system in the multivariate case is discussed also. In this context, it is shown that some multivariate interpolation spaces share properties of univariate Haar-Chebyshev systems. We study also the problem of best one-sided multivariate L 1-approximation by sums of univariate functions. Explicit constructions of best one-sided L1-approximants give rise to well-known and new inequalities.