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http://hdl.handle.net/10397/74212
| Title: | Runge–Kutta time discretization of nonlinear parabolic equations studied via discrete maximal parabolic regularity | Authors: | Kunstmann, PC Li, B Lubich, C |
Issue Date: | Oct-2018 | Source: | Foundations of computational mathematics, Oct. 2018, p. 1109-1130 | Abstract: | For a large class of fully nonlinear parabolic equations, which include gradient flows for energy functionals that depend on the solution gradient, the semidiscretization in time by implicit Runge–Kutta methods such as the Radau IIA methods of arbitrary order is studied. Error bounds are obtained in the (Formula presented.) norm uniformly on bounded time intervals and, with an improved approximation order, in the parabolic energy norm. The proofs rely on discrete maximal parabolic regularity. This is used to obtain (Formula presented.) estimates, which are the key to the numerical analysis of these problems. | Keywords: | Error bounds Gradient flow Maximal parabolic regularity Nonlinear parabolic equation Runge–Kutta method Stability |
Publisher: | Springer | Journal: | Foundations of computational mathematics | ISSN: | 1615-3375 | DOI: | 10.1007/s10208-017-9364-x | Rights: | © SFoCM 2017 This version of the article has been accepted for publication, after peer review (when applicable) and is subject to Springer Nature’s AM terms of use (https://www.springernature.com/gp/open-research/policies/accepted-manuscript-terms), but is not the Version of Record and does not reflect post-acceptance improvements, or any corrections. The Version of Record is available online at: http://dx.doi.org/10.1007/s10208-017-9364-x |
| Appears in Collections: | Journal/Magazine Article |
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| Kunstmann_Runge-Kutttime_Discretizatinonlinear_Parabolic.pdf | Pre-Published version | 380.96 kB | Adobe PDF | View/Open |
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