Cubature on C^1 space
We explore in this paper cubature formulas over the space of functions having a first continuous derivative, i.e., C^1. We show that known cubature formulas are not optimal in this case and explain what is the origin of the loss of optimality and how to construct optimal ones; to illustrate we give cubature formulas up to (including) order 9.
|Date of creation:||01 Jun 2013|
|Date of revision:|
|Publication status:||Published in Kristian Bredies, Christian Clason, Karl Kunisch, Gregory Winckel. Control and Optimization with PDE Constraints, Springer Basel, pp.159-172, 2013, International Series of Numerical Mathematics, 978-3-0348-0630-5. <10.1007/978-3-0348-0631-2_9>|
|Note:||View the original document on HAL open archive server: https://hal.archives-ouvertes.fr/hal-00660875v2|
|Contact details of provider:|| Web page: https://hal.archives-ouvertes.fr/|
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