Comparison of approximate shape gradients
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| 024 | 7 | 0 | |a 10.1007/s10543-014-0515-z |2 doi |
| 035 | |a (NATIONALLICENCE)springer-10.1007/s10543-014-0515-z | ||
| 245 | 0 | 0 | |a Comparison of approximate shape gradients |h [Elektronische Daten] |c [R. Hiptmair, A. Paganini, S. Sargheini] |
| 520 | 3 | |a Shape gradients of PDE constrained shape functionals can be stated in two equivalent ways. Both rely on the solutions of two boundary value problems (BVPs), but one involves integrating their traces on the boundary of the domain, while the other evaluates integrals in the volume. Usually, the two BVPs can only be solved approximately, for instance, by finite element methods. However, when used with finite element solutions, the equivalence of the two formulas breaks down. By means of a comprehensive convergence analysis, we establish that the volume based expression for the shape gradient generally offers better accuracy in a finite element setting. The results are confirmed by several numerical experiments. | |
| 540 | |a Springer Science+Business Media Dordrecht, 2014 | ||
| 690 | 7 | |a Shape gradients |2 nationallicence | |
| 690 | 7 | |a Shape calculus |2 nationallicence | |
| 690 | 7 | |a Finite element approximations |2 nationallicence | |
| 690 | 7 | |a Duality techniques |2 nationallicence | |
| 700 | 1 | |a Hiptmair |D R. |u Seminar for Applied Mathematics, ETH Zurich, Zurich, Switzerland |4 aut | |
| 700 | 1 | |a Paganini |D A. |u Seminar for Applied Mathematics, ETH Zurich, Zurich, Switzerland |4 aut | |
| 700 | 1 | |a Sargheini |D S. |u Seminar for Applied Mathematics, ETH Zurich, Zurich, Switzerland |4 aut | |
| 773 | 0 | |t BIT Numerical Mathematics |d Springer Netherlands |g 55/2(2015-06-01), 459-485 |x 0006-3835 |q 55:2<459 |1 2015 |2 55 |o 10543 | |
| 856 | 4 | 0 | |u https://doi.org/10.1007/s10543-014-0515-z |q text/html |z Onlinezugriff via DOI |
| 898 | |a BK010053 |b XK010053 |c XK010000 | ||
| 900 | 7 | |a Metadata rights reserved |b Springer special CC-BY-NC licence |2 nationallicence | |
| 908 | |D 1 |a research-article |2 jats | ||
| 949 | |B NATIONALLICENCE |F NATIONALLICENCE |b NL-springer | ||
| 950 | |B NATIONALLICENCE |P 856 |E 40 |u https://doi.org/10.1007/s10543-014-0515-z |q text/html |z Onlinezugriff via DOI | ||
| 950 | |B NATIONALLICENCE |P 700 |E 1- |a Hiptmair |D R. |u Seminar for Applied Mathematics, ETH Zurich, Zurich, Switzerland |4 aut | ||
| 950 | |B NATIONALLICENCE |P 700 |E 1- |a Paganini |D A. |u Seminar for Applied Mathematics, ETH Zurich, Zurich, Switzerland |4 aut | ||
| 950 | |B NATIONALLICENCE |P 700 |E 1- |a Sargheini |D S. |u Seminar for Applied Mathematics, ETH Zurich, Zurich, Switzerland |4 aut | ||
| 950 | |B NATIONALLICENCE |P 773 |E 0- |t BIT Numerical Mathematics |d Springer Netherlands |g 55/2(2015-06-01), 459-485 |x 0006-3835 |q 55:2<459 |1 2015 |2 55 |o 10543 | ||