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Sobolev Gradients And Differential Equations
- Collana:
- Lecture Notes In Mathematics
- EAN:
9783642040405
- ISBN:
3642040403
- Pagine:
- 289
- Formato:
- Paperback
- Lingua:
- Tedesco
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Descrizione Sobolev Gradients And Differential Equations
A Sobolev gradient of a real-valued functional on a Hilbert space is a gradient of that functional taken relative to an underlying Sobolev norm. This book shows how descent methods using such gradients allow a unified treatment of a wide variety of problems in differential equations. For discrete versions of partial differential equations, corresponding Sobolev gradients are seen to be vastly more efficient than ordinary gradients. In fact, descent methods with these gradients generally scale linearly with the number of grid points, in sharp contrast with the use of ordinary gradients. Aside from the first edition of this work, this is the only known account of Sobolev gradients in book form.
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