Abstract
The mathematical description of problems involving discontinuities requires using function spaces that extend the concept of weak derivatives. The gradients of functions of bounded variation are certain measures and the functions may jump across lower-dimensional subsets. The properties of this function space enable the mathematical modeling of fracture and crack formation of materials within the framework of the calculus of variations. Qualitatively, similar model problems arise in image processing to formulate denoising or segmentation of an image. Convergence, error estimation, iterative solution, and implementation of finite element discretizations of these model problems are investigated in this chapter.
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Bartels, S. (2015). Free Discontinuities. In: Numerical Methods for Nonlinear Partial Differential Equations. Springer Series in Computational Mathematics, vol 47. Springer, Cham. https://doi.org/10.1007/978-3-319-13797-1_10
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DOI: https://doi.org/10.1007/978-3-319-13797-1_10
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