Abstract
In this chapter, the nonlinear problem class of parabolic type which will be studied is introduced in a Hilbert space setting. The main assumptions are formulated in terms of sectorial operators which are negative infinitesimal generators of analytic semigroups. They are general enough to cover a huge class of important applications. Our setting is taken from Lubich and Ostermann [103], where a rigorous analysis of linearly implicit time discretizations applied to nonlinear parabolic equations is given. The assumptions are slightly extended to a family of operators A(t, w(t)), where w(t) is varying in a neighbourhood of the solution. This allows later the study of spatial projection errors.
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© 2001 Springer-Verlag Berlin Heidelberg
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Lang, J. (2001). The Continuous Problem and Its Discretization in Time. In: Adaptive Multilevel Solution of Nonlinear Parabolic PDE Systems. Lecture Notes in Computational Science and Engineering, vol 16. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-662-04484-1_2
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DOI: https://doi.org/10.1007/978-3-662-04484-1_2
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-08747-9
Online ISBN: 978-3-662-04484-1
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