K-convergence as a new tool in numerical analysis

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. E-ISSN 1464-3642
R&D Projects: GA ČR(CZ) GA18-05974S
Institutional support: RVO:67985840
Keywords : K-convergence * numerical analysis
OECD category: Pure mathematics
Impact factor: 2.601, year: 2020
Method of publishing: Limited access
https://doi.org/10.1093/imanum/drz045

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.
Permanent Link: http://hdl.handle.net/11104/0311771