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Continuous and disc...
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Holm, BärbelKTH,Beräkningsvetenskap och beräkningsteknik (CST)
(author)
Continuous and discontinuous Galerkin time stepping methods for nonlinear initial value problems with application to finite time blow-up
- Article/chapterEnglish2018
Publisher, publication year, extent ...
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2017-10-05
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SPRINGER HEIDELBERG,2018
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Numbers
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LIBRIS-ID:oai:DiVA.org:kth-225293
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https://urn.kb.se/resolve?urn=urn:nbn:se:kth:diva-225293URI
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https://doi.org/10.1007/s00211-017-0918-2DOI
Supplementary language notes
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Language:English
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Summary in:English
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Subject category:ref swepub-contenttype
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Subject category:art swepub-publicationtype
Notes
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QC 20180406
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We consider continuous and discontinuous Galerkin time stepping methods of arbitrary order as applied to first-order initial value ordinary differential equation problems in real Hilbert spaces. Our only assumption is that the nonlinearities are continuous; in particular, we include the case of unbounded nonlinear operators. Specifically, we develop new techniques to prove general Peano-type existence results for discrete solutions. In particular, our results show that the existence of solutions is independent of the local approximation order, and only requires the local time steps to be sufficiently small (independent of the polynomial degree). The uniqueness of (local) solutions is addressed as well. In addition, our theory is applied to finite time blow-up problems with nonlinearities of algebraic growth. For such problems we develop a time step selection algorithm for the purpose of numerically computing the blow-up time, and provide a convergence result.
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Wihler, Thomas P.Univ Bern, Math Inst, Sidlerstr 5, CH-3012 Bern, Switzerland.
(author)
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KTHBeräkningsvetenskap och beräkningsteknik (CST)
(creator_code:org_t)
Related titles
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In:Numerische Mathematik: SPRINGER HEIDELBERG138:3, s. 767-7990029-599X0945-3245
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