Efficient goal-oriented global error estimators for BDF methods using discrete adjoints
In this paper we develop new goal-oriented global error estimators for variable multistep backward differentiation formulae (BDF) methods. These estimators use, for the first time in the context of multistep methods, discrete adjoints computed by adjoint differentiation of the nominal integration sc...
Saved in:
| Main Author: | |
|---|---|
| Format: | Article (Journal) |
| Language: | English |
| Published: |
2017
|
| In: |
Journal of computational and applied mathematics
Year: 2016, Volume: 316, Pages: 195-212 |
| ISSN: | 1879-1778 |
| DOI: | 10.1016/j.cam.2016.09.032 |
| Online Access: | Verlag, Volltext: http://www.sciencedirect.com/science/article/pii/S0377042716304526 Verlag, Volltext: http://dx.doi.org/10.1016/j.cam.2016.09.032 
|
| Author Notes: | Dörte Jando |
MARC
| LEADER | 00000caa a2200000 c 4500 | ||
|---|---|---|---|
| 001 | 1577485823 | ||
| 003 | DE-627 | ||
| 005 | 20220814190458.0 | ||
| 007 | cr uuu---uuuuu | ||
| 008 | 180711r20172016xx |||||o 00| ||eng c | ||
| 024 | 7 | |a 10.1016/j.cam.2016.09.032 |2 doi | |
| 035 | |a (DE-627)1577485823 | ||
| 035 | |a (DE-576)507485823 | ||
| 035 | |a (DE-599)BSZ507485823 | ||
| 035 | |a (OCoLC)1341013675 | ||
| 040 | |a DE-627 |b ger |c DE-627 |e rda | ||
| 041 | |a eng | ||
| 084 | |a 27 |2 sdnb | ||
| 100 | 1 | |a Jando, Dörte |e VerfasserIn |0 (DE-588)1031176632 |0 (DE-627)735791910 |0 (DE-576)378611410 |4 aut | |
| 245 | 1 | 0 | |a Efficient goal-oriented global error estimators for BDF methods using discrete adjoints |c Dörte Jando |
| 264 | 1 | |c 2017 | |
| 300 | |a 18 | ||
| 336 | |a Text |b txt |2 rdacontent | ||
| 337 | |a Computermedien |b c |2 rdamedia | ||
| 338 | |a Online-Ressource |b cr |2 rdacarrier | ||
| 500 | |a Available online 1 October 2016 | ||
| 500 | |a Gesehen am 11.07.2018 | ||
| 520 | |a In this paper we develop new goal-oriented global error estimators for variable multistep backward differentiation formulae (BDF) methods. These estimators use, for the first time in the context of multistep methods, discrete adjoints computed by adjoint differentiation of the nominal integration scheme. The derivation is based on the recently developed Petrov-Galerkin finite element formulation of BDF methods and their discrete adjoint schemes and makes use of the dual weighted residual methodology. Defect integrals or local truncation errors are used as local error quantities. We prove the asymptotic correctness and optimal convergence of the novel estimators for the one-step BDF method. For multistep BDF methods using a selfstarting procedure we show that the estimator with defect integrals converges but suboptimal and that its effectivity index converges to an offset value. On the other hand, the estimator with local truncation errors is again asymptotically correct and of optimal order. We confirm these results numerically. With a real-world example from chemical engineering, we give promising numerical results for the estimation accuracy in variable BDF-type methods with changing orders and stepsizes. Finally, we give a first use of the novel estimators for goal-oriented global error control of a challenging stiff test problem. | ||
| 534 | |c 2016 | ||
| 650 | 4 | |a BDF methods | |
| 650 | 4 | |a Discrete adjoints | |
| 650 | 4 | |a Dual weighted residual methodology | |
| 650 | 4 | |a Global error estimation | |
| 650 | 4 | |a Petrov-Galerkin discretization | |
| 773 | 0 | 8 | |i Enthalten in |t Journal of computational and applied mathematics |d Amsterdam : Elsevier, 1975 |g 316(2017), Seite 195-212 |h Online-Ressource |w (DE-627)266889204 |w (DE-600)1468806-2 |w (DE-576)075962373 |x 1879-1778 |7 nnas |a Efficient goal-oriented global error estimators for BDF methods using discrete adjoints |
| 773 | 1 | 8 | |g volume:316 |g year:2017 |g pages:195-212 |g extent:18 |a Efficient goal-oriented global error estimators for BDF methods using discrete adjoints |
| 856 | 4 | 0 | |u http://www.sciencedirect.com/science/article/pii/S0377042716304526 |x Verlag |3 Volltext |
| 856 | 4 | 0 | |u http://dx.doi.org/10.1016/j.cam.2016.09.032 |x Verlag |x Resolving-System |3 Volltext |
| 951 | |a AR | ||
| 992 | |a 20180711 | ||
| 993 | |a Article | ||
| 994 | |a 2017 | ||
| 998 | |g 1031176632 |a Jando, Dörte |m 1031176632:Jando, Dörte |d 700000 |d 708000 |e 700000PJ1031176632 |e 708000PJ1031176632 |k 0/700000/ |k 1/700000/708000/ |p 1 |x j |y j | ||
| 999 | |a KXP-PPN1577485823 |e 3017280985 | ||
| BIB | |a Y | ||
| SER | |a journal | ||
| JSO | |a {"name":{"displayForm":["Dörte Jando"]},"id":{"eki":["1577485823"],"doi":["10.1016/j.cam.2016.09.032"]},"origin":[{"dateIssuedKey":"2017","dateIssuedDisp":"2017"}],"relHost":[{"language":["eng"],"recId":"266889204","type":{"media":"Online-Ressource","bibl":"periodical"},"note":["Gesehen am 04.06.2020"],"disp":"Efficient goal-oriented global error estimators for BDF methods using discrete adjointsJournal of computational and applied mathematics","part":{"year":"2017","pages":"195-212","volume":"316","text":"316(2017), Seite 195-212","extent":"18"},"pubHistory":["1.1975 -"],"title":[{"title":"Journal of computational and applied mathematics","title_sort":"Journal of computational and applied mathematics"}],"physDesc":[{"extent":"Online-Ressource"}],"id":{"eki":["266889204"],"zdb":["1468806-2"],"issn":["1879-1778"]},"origin":[{"dateIssuedDisp":"1975-","publisher":"Elsevier ; North-Holland","dateIssuedKey":"1975","publisherPlace":"Amsterdam ; Amsterdam [u.a.]"}]}],"physDesc":[{"extent":"18 S."}],"person":[{"role":"aut","roleDisplay":"VerfasserIn","display":"Jando, Dörte","given":"Dörte","family":"Jando"}],"title":[{"title":"Efficient goal-oriented global error estimators for BDF methods using discrete adjoints","title_sort":"Efficient goal-oriented global error estimators for BDF methods using discrete adjoints"}],"recId":"1577485823","language":["eng"],"note":["Available online 1 October 2016","Gesehen am 11.07.2018"],"type":{"media":"Online-Ressource","bibl":"article-journal"}} | ||
| SRT | |a JANDODOERTEFFICIENTG2017 | ||