000903291 001__ 903291 000903291 005__ 20230310131315.0 000903291 0247_ $$2doi$$a10.2140/camcos.2021.16.227 000903291 0247_ $$2ISSN$$a1559-3940 000903291 0247_ $$2ISSN$$a2157-5452 000903291 0247_ $$2Handle$$a2128/29361 000903291 0247_ $$2WOS$$aWOS:000752484200003 000903291 037__ $$aFZJ-2021-04987 000903291 082__ $$a510 000903291 1001_ $$0P:(DE-Juel1)164486$$aKremling, Gitte$$b0 000903291 245__ $$aConvergence of multilevel spectral deferred corrections 000903291 260__ $$aBerkeley, Calif.$$bMathematical Sciences Publishers$$c2021 000903291 3367_ $$2DRIVER$$aarticle 000903291 3367_ $$2DataCite$$aOutput Types/Journal article 000903291 3367_ $$0PUB:(DE-HGF)16$$2PUB:(DE-HGF)$$aJournal Article$$bjournal$$mjournal$$s1638864849_11468 000903291 3367_ $$2BibTeX$$aARTICLE 000903291 3367_ $$2ORCID$$aJOURNAL_ARTICLE 000903291 3367_ $$00$$2EndNote$$aJournal Article 000903291 520__ $$aThe spectral deferred correction (SDC) method is a class of iterative solvers for ordinary differential equations (ODEs). It can be interpreted as a preconditioned Picard iteration for the collocation problem. The convergence of this method is well known, for suitable problems it gains one order per iteration up to the order of the quadrature method of the collocation problem provided. This appealing feature enables an easy creation of flexible, high-order accurate methods for ODEs. A variation of SDC are multilevel spectral deferred corrections (MLSDC). Here, iterations are performed on a hierarchy of levels and an FAS correction term, as in nonlinear multigrid methods, couples solutions on different levels. While there are several numerical examples which show its capabilities and efficiency, a theoretical convergence proof is still missing. We address this issue. A proof of the convergence of MLSDC, including the determination of the convergence rate in the time-step size, will be given and the results of the theoretical analysis will be numerically demonstrated. It turns out that there are restrictions for the advantages of this method over SDC regarding the convergence rate. 000903291 536__ $$0G:(DE-HGF)POF4-5111$$a5111 - Domain-Specific Simulation Data Life Cycle Labs (SDLs) and Research Groups (POF4-511)$$cPOF4-511$$fPOF IV$$x0 000903291 536__ $$0G:(GEPRIS)450829162$$aDFG project 450829162 - Raum-Zeit-parallele Simulation multimodale Energiesystemen (450829162)$$c450829162$$x1 000903291 588__ $$aDataset connected to CrossRef, Journals: juser.fz-juelich.de 000903291 7001_ $$0P:(DE-Juel1)132268$$aSpeck, Robert$$b1$$eCorresponding author$$ufzj 000903291 773__ $$0PERI:(DE-600)2270595-8$$a10.2140/camcos.2021.16.227$$gVol. 16, no. 2, p. 227 - 265$$n2$$p227 - 265$$tCommunications in applied mathematics and computational science$$v16$$x1559-3940$$y2021 000903291 8564_ $$uhttps://juser.fz-juelich.de/record/903291/files/camcos-v16-n2-p03-s.pdf$$yOpenAccess 000903291 909CO $$ooai:juser.fz-juelich.de:903291$$pdnbdelivery$$pdriver$$pVDB$$popen_access$$popenaire 000903291 9101_ $$0I:(DE-588b)5008462-8$$6P:(DE-Juel1)132268$$aForschungszentrum Jülich$$b1$$kFZJ 000903291 9131_ $$0G:(DE-HGF)POF4-511$$1G:(DE-HGF)POF4-510$$2G:(DE-HGF)POF4-500$$3G:(DE-HGF)POF4$$4G:(DE-HGF)POF$$9G:(DE-HGF)POF4-5111$$aDE-HGF$$bKey Technologies$$lEngineering Digital Futures – Supercomputing, Data Management and Information Security for Knowledge and Action$$vEnabling Computational- & Data-Intensive Science and Engineering$$x0 000903291 9141_ $$y2021 000903291 915__ $$0StatID:(DE-HGF)0200$$2StatID$$aDBCoverage$$bSCOPUS$$d2021-01-27 000903291 915__ $$0StatID:(DE-HGF)0300$$2StatID$$aDBCoverage$$bMedline$$d2021-01-27 000903291 915__ $$0StatID:(DE-HGF)1150$$2StatID$$aDBCoverage$$bCurrent Contents - Physical, Chemical and Earth Sciences$$d2021-01-27 000903291 915__ $$0StatID:(DE-HGF)0113$$2StatID$$aWoS$$bScience Citation Index Expanded$$d2021-01-27 000903291 915__ $$0StatID:(DE-HGF)0150$$2StatID$$aDBCoverage$$bWeb of Science Core Collection$$d2021-01-27 000903291 915__ $$0StatID:(DE-HGF)9900$$2StatID$$aIF < 5$$d2021-01-27 000903291 915__ $$0StatID:(DE-HGF)0510$$2StatID$$aOpenAccess 000903291 915__ $$0StatID:(DE-HGF)0100$$2StatID$$aJCR$$bCOMM APP MATH COM SC : 2019$$d2021-01-27 000903291 915__ $$0StatID:(DE-HGF)0160$$2StatID$$aDBCoverage$$bEssential Science Indicators$$d2021-01-27 000903291 915__ $$0StatID:(DE-HGF)0199$$2StatID$$aDBCoverage$$bClarivate Analytics Master Journal List$$d2021-01-27 000903291 920__ $$lyes 000903291 9201_ $$0I:(DE-Juel1)JSC-20090406$$kJSC$$lJülich Supercomputing Center$$x0 000903291 980__ $$ajournal 000903291 980__ $$aVDB 000903291 980__ $$aUNRESTRICTED 000903291 980__ $$aI:(DE-Juel1)JSC-20090406 000903291 9801_ $$aFullTexts