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Error analysis of implicit Euler methods for quasilinear hyperbolic evolution systems

Hochbruck, Marlis; Pažur, Tomislav

Abstract: In this paper we study the convergence of the semi-implicit and the implicit Euler methods for the time integration of abstract, quasilinear hyperbolic evolution equations. The analytical framework considered here includes certain quasilinear Maxwell's and wave equations as special cases. Our analysis shows that the Euler approximations are well-posed and convergent of order one. The techniques will be the basis for the future investigation of higher order time integration methods and full discretizations of certain quasilinear hyperbolic problems.

Zugehörige Institution(en) am KIT Institut für Angewandte und Numerische Mathematik (IANM)
Sonderforschungsbereich 1173 (SFB 1173)
Publikationstyp Forschungsbericht
Jahr 2016
Sprache Englisch
Identifikator DOI(KIT): 10.5445/IR/1000053752
ISSN: 2365-662X
URN: urn:nbn:de:swb:90-537523
KITopen ID: 1000053752
Verlag KIT, Karlsruhe
Umfang 22 S.
Serie CRC 1173 ; 2016/9
Schlagworte hyperbolic evolution equations, quasilinear Maxwell’s equations, quasilinear wave equation, implicit Euler method, semi-implicit Euler method, well-posedness, error analysis, time integration
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