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Erschienen in:
2021 | OriginalPaper | Buchkapitel
11. An Outlook to Nonlinear Partial Differential Equations
verfasst von : Peter Knabner, Lutz Angermann
Erschienen in: Numerical Methods for Elliptic and Parabolic Partial Differential Equations
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Abstract
Despite the concentration of most of the book on linear boundary value problems and their discretizations, many real-world models are rather nonlinear elliptic or parabolic boundary value problems with various types of nonlinearities. To be specific, we restrict ourselves to the formulation in divergence form (3.36) and its time-dependent counterpart and the classical FEM based on Chapter 2 and Chapter 3. Let \(a, \ell \) be the forms from (3.36) to (3.39), a first nonlinear (here: semilinear) boundary value problem reads.