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  • Open Daily: 10am - 10pm
    Alley-side Pickup: 10am - 7pm

    3038 Hennepin Ave Minneapolis, MN
    612-822-4611

Open Daily: 10am - 10pm | Alley-side Pickup: 10am - 7pm
3038 Hennepin Ave Minneapolis, MN
612-822-4611
Sobolev Gradients and Differential Equations

Sobolev Gradients and Differential Equations

Neuberger, John

Paperback

Series: Lecture Notes in Mathematics, Book 1670

General Mathematics

ISBN10: 3642040403
ISBN13: 9783642040405
Publisher: Springer
Published: Dec 1 2009
Pages: 289
Weight: 0.97
Height: 0.65 Width: 6.14 Depth: 9.21
Language: English

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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