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Title: Higher-order exponential integrators for quasi-linear parabolic problems. Part II: Convergence
Authors: González Fernández, Cesáreo
Thalhammer, Mechthild
Issue Date: 2016
Citation: SIAM Journal on Numerical Analysis 54-5 (2016), pp. 2868-2888
Abstract: In this work, the convergence analysis of explicit exponential time integrators based on general linear methods for quasi-linear parabolic initial boundary value problems is pursued. Compared to other types of exponential integrators encountering rather severe order reductions, in general, the considered class of exponential general linear methods provides the possibility of constructing schemes that retain higher-order accuracy in time when applied to quasi-linear parabolic problems. In view of practical applications, the case of variable time step sizes is incorporated. The convergence analysis is based upon two fundamental ingredients. The needed stability bounds, obtained under mild restrictions on the ratios of subsequent time step sizes, have been deduced in the recent work [C. González and M. Thalhammer, SIAM J. Numer. Anal., 53 (2015), pp. 701--719]. The core of the present work is devoted to the derivation of suitable local and global error representations. In conjunction with the stability bounds, a convergence result is established.
ISSN: 0036-1429
Peer Review: SI
Sponsor: Ministerio de Economía, Industria y Competitividad, proyecto MTM2013-46553-C3-1-P y Austrian Science Fund (FWF), projects P21620-N13 and P28645-N35.
Publisher Version:
Language: eng
Rights: info:eu-repo/semantics/openAccess
Appears in Collections:DEP51 - Artículos de revista

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