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  • 1. Babuska, I.
    et al.
    Nobile, F.
    Tempone, Raul
    Reliability of computational science2007In: Numerical Methods for Partial Differential Equations, ISSN 0749-159X, E-ISSN 1098-2426, Vol. 23, no 4, p. 753-784Article in journal (Refereed)
    Abstract [en]

    Today's computers allow us to simulate large, complex physical problems. Many times the mathematical models describing such problems are based on a relatively small amount of available information such as experimental measurements. The question arises whether the computed data could be used as the basis for decision in critical engineering, economic, and medicine applications. The representative list of engineering accidents occurred in the past years and their reasons illustrate the question. The paper describes a general framework for verification and validation (V&V) which deals with this question. The framework is then applied to an illustrative engineering problem, in which the basis for decision is a specific quantity of interest, namely the probability that the quantity does not exceed a given value. The V&V framework is applied and explained in detail. The result of the analysis is the computation of the failure probability as well as a quantification of the confidence in the computation, depending on the amount of available experimental data.

  • 2.
    Efraimsson, Gunilla
    KTH, Superseded Departments, Numerical Analysis and Computer Science, NADA.
    A numerical method for the first-order wave equation with discontinuous initial data1998In: Numerical Methods for Partial Differential Equations, ISSN 0749-159X, E-ISSN 1098-2426, Vol. 138, no 3, p. 353-365Article in journal (Refereed)
    Abstract [en]

    We introduce a method, constructed such that numerical solutions of the wave equation are well behaved when the solutions also contain discontinuities. The wave equation serves as a model problem for the Euler equations when the solution contains a contact discontinuity. Numerical computations of linear equations and the Euler equations in one and two dimensions are presented

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