Abstract
This survey consists of five parts. In the first section we describe a model problem and a two-level algorithm in order to motivate the multilevel approach. In Section 2 an abstract multilevel algorithm is described and analyzed under some regularity assumptions. An analysis under less stringent assumptions is given in Section 3. Non-nested spaces and varying forms are treated in Section 4. Finally, we show how the multilevel framework provides computationally efficient realizations of norms on Sobolev scales.
Keywords
- Sobolev Space
- Domain Decomposition
- Multigrid Method
- Extension Operator
- Nodal Basis
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© 2003 Springer-Verlag Berlin Heidelberg
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Bramble, J.H. (2003). Multilevel Methods in Finite Elements. In: Canuto, C. (eds) Multiscale Problems and Methods in Numerical Simulations. Lecture Notes in Mathematics, vol 1825. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-39810-3_3
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DOI: https://doi.org/10.1007/978-3-540-39810-3_3
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Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-20099-4
Online ISBN: 978-3-540-39810-3
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