Nonlinear evolution governed by accretive operators in Banach spaces: error control and applications (Articolo in rivista)

Type
Label
  • Nonlinear evolution governed by accretive operators in Banach spaces: error control and applications (Articolo in rivista) (literal)
Anno
  • 2006-01-01T00:00:00+01:00 (literal)
Http://www.cnr.it/ontology/cnr/pubblicazioni.owl#doi
  • 10.1142/S0218202506001224 (literal)
Alternative label
  • R. H. Nochetto; G. Savare (2006)
    Nonlinear evolution governed by accretive operators in Banach spaces: error control and applications
    in Mathematical models and methods in applied sciences
    (literal)
Http://www.cnr.it/ontology/cnr/pubblicazioni.owl#autori
  • R. H. Nochetto; G. Savare (literal)
Pagina inizio
  • 439 (literal)
Pagina fine
  • 477 (literal)
Http://www.cnr.it/ontology/cnr/pubblicazioni.owl#url
  • http://www.worldscinet.com/m3as/16/1603/S0218202506001224.html (literal)
Http://www.cnr.it/ontology/cnr/pubblicazioni.owl#numeroVolume
  • 16 (literal)
Rivista
Http://www.cnr.it/ontology/cnr/pubblicazioni.owl#numeroFascicolo
  • 3 (literal)
Note
  • ISI Web of Science (WOS) (literal)
  • Scopu (literal)
  • Mathematical Reviews on the web (MathSciNet) (literal)
  • Google Scholar (literal)
Http://www.cnr.it/ontology/cnr/pubblicazioni.owl#affiliazioni
  • R. H. Nochetto: Department of Mathematics and Institute for Physical Science and Technology, University of Maryland College Park, MD 20742, USA G. Savare: Dipartimento di Matematica, Universita` di Pavia, and I.M.A.T.I., C.N.R., Via Ferrata 1, 27100 Pavia, Italy (literal)
Titolo
  • Nonlinear evolution governed by accretive operators in Banach spaces: error control and applications (literal)
Abstract
  • Nonlinear evolution equations governed by m-accretive operators in Banach spaces are discretized via the backward or forward Euler methods with variable stepsize. Computable a posteriori error estimates are derived in terms of the discrete solution and data, and shown to converge with optimal order O(??). Applications to scalar conservation laws and degenerate parabolic equations (with or without hysteresis) in L1, as well as to Hamilton-Jacobi equations are given. The error analysis relies on a comparison principle, for the novel notion of relaxed solutions, which combines and simplifies techniques of Benilan and Kruzkov. Our results provide a unified framework for existence, uniqueness and error analysis, and yield a new proof of the celebrated Crandall-Liggett error estimate. (literal)
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