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K-convergence as a new tool in numerical analysis

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    0533370 - MÚ 2021 RIV GB eng J - Journal Article
    Feireisl, Eduard - Lukáčová-Medviďová, M. - Mizerová, Hana
    K-convergence as a new tool in numerical analysis.
    IMA Journal of Numerical Analysis. Roč. 40, č. 4 (2020), s. 2227-2255. ISSN 0272-4979
    R&D Projects: GA ČR(CZ) GA18-05974S
    Institutional support: RVO:67985840
    Keywords : K-convergence * numerical analysis
    Subject RIV: BA - General Mathematics
    OBOR OECD: Pure mathematics
    Impact factor: 2.275, year: 2019

    We adapt the concept of K-convergence of Young measures to the sequences of approximate solutions resulting from numerical schemes. We obtain new results on pointwise convergence of numerical solutions in the case when solutions of the limit continuous problem possess minimal regularity. We apply the abstract theory to a finite volume method for the isentropic Euler system describing the motion of a compressible inviscid fluid. The result can be seen as a nonlinear version of the fundamental Lax equivalence theorem.
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