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Paper Citation Record · LEDGER

An Augmented Lagrangian Preconditioner for Navier--Stokes Equations with Runge--Kutta in Time

As of 8 August 2026, this Paper Citation Record lists 52 of 52 outbound references and 0 inbound Pith citation observations for arXiv:2506.04451.

A citation records a reference. It does not transfer a finding from one paper to another.

pith.paper-citation-record.v1
2506.04451 v1

Coverage vector

measured 52 of 52 reference resolution

Typed states for the displayed outbound observations.

Source: paper_references, paper_reference_links, observed 2026-08-07T10:50:51.469072Z

measured 52 of 52 standing notices

One-hop event checks from named stored sources.

Source: scholarly_work_events, retraction_status_cache, observed 2026-08-08T06:32:00.761636+00:00

measured 0 of 0 inbound itemization

Pith citing papers itemized under the disclosed page cap.

Source: paper_references, paper_reference_links

measured 0 of 1 external citation measurements

A source-named dated measurement, never combined with another source.

Source: cited_works

Reference resolution

52 of 52 outbound references displayed

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  • verified fuzzy30
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External citation measurements

No source-named external measurement is stored.

Outbound references

Observation c3050ab6-2254-42ea-8c80-5f47beaf2940 · outbound

This paper cites Abu-Labdeh, S.

An Augmented Lagrangian Preconditioner for Navier--Stokes Equations with Runge--Kutta in Time Abu-Labdeh, S

Reference 1

Resolution
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Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.

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Observation 2b55eda6-ad5c-440f-b062-70b504d1ae00 · outbound

This paper cites Axelsson, I.

An Augmented Lagrangian Preconditioner for Navier--Stokes Equations with Runge--Kutta in Time Axelsson, I

Reference 2

Resolution
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Observation 26a989a4-b335-47aa-8317-979b3240fb7b · outbound

This paper cites Becker and M.

An Augmented Lagrangian Preconditioner for Navier--Stokes Equations with Runge--Kutta in Time Becker and M

Reference 3

Resolution
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Source-reported events for the cited work

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Observation 6e519d5d-c414-4164-a96a-102a2e0e0e6b · outbound

This paper cites Becker and B.

An Augmented Lagrangian Preconditioner for Navier--Stokes Equations with Runge--Kutta in Time Becker and B

Reference 4

Resolution
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Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.

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Observation e0e1cbe5-4977-4285-b86e-a6f1249a3e21 · outbound

This paper cites Benzi, G.

An Augmented Lagrangian Preconditioner for Navier--Stokes Equations with Runge--Kutta in Time Benzi, G

Reference 5

Resolution
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Source-reported events for the cited work

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Observation 7d6dd4ab-8777-4827-bceb-ef87b61e0040 · outbound

This paper cites Benzi and M.

An Augmented Lagrangian Preconditioner for Navier--Stokes Equations with Runge--Kutta in Time Benzi and M

Reference 6

Resolution
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Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.

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Observation c66c57d1-258c-441f-9ae2-34c3611fe24d · outbound

This paper cites Benzi and M.

An Augmented Lagrangian Preconditioner for Navier--Stokes Equations with Runge--Kutta in Time Benzi and M

Reference 7

Resolution
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Source-reported events for the cited work

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Observation fdfb6fc5-6d56-43a6-b440-d54f90e1f62f · outbound

This paper cites Boonen, J.

An Augmented Lagrangian Preconditioner for Navier--Stokes Equations with Runge--Kutta in Time Boonen, J

Reference 8

Resolution
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Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.

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Observation f10e02f9-4115-4c95-966c-23661b62b834 · outbound

This paper cites Boyle, M.

An Augmented Lagrangian Preconditioner for Navier--Stokes Equations with Runge--Kutta in Time Boyle, M

Reference 9

Resolution
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Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.

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Observation 41ff88eb-f23d-4a4a-a983-14ef054e5d20 · outbound

This paper cites Braack and E.

An Augmented Lagrangian Preconditioner for Navier--Stokes Equations with Runge--Kutta in Time Braack and E

Reference 10

Resolution
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Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.

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Observation acfb4600-e823-4ecf-a477-f13686efef53 · outbound

This paper cites an unresolved cited work.

An Augmented Lagrangian Preconditioner for Navier--Stokes Equations with Runge--Kutta in Time Unresolved cited work

Reference 11

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Observation d6fb7586-1d97-4791-b328-3f0bcdbf2143 · outbound

This paper cites an unresolved cited work.

An Augmented Lagrangian Preconditioner for Navier--Stokes Equations with Runge--Kutta in Time Unresolved cited work

Reference 12

Resolution
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Source-reported events for the cited work

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Observation e064105a-0f30-4fce-9c31-13e4ebdfbcec · outbound

This paper cites an unresolved cited work.

An Augmented Lagrangian Preconditioner for Navier--Stokes Equations with Runge--Kutta in Time Unresolved cited work

Reference 13

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Source-reported events for the cited work

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Observation 9f356bc4-1173-4501-8ad6-07930c20d245 · outbound

This paper cites an unresolved cited work.

An Augmented Lagrangian Preconditioner for Navier--Stokes Equations with Runge--Kutta in Time Unresolved cited work

Reference 14

Resolution
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Source-reported events for the cited work

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Observation ba6f9714-7bd9-4e38-942b-96925ad20a29 · outbound

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An Augmented Lagrangian Preconditioner for Navier--Stokes Equations with Runge--Kutta in Time Unresolved cited work

Reference 15

Resolution
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Source-reported events for the cited work

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Observation aa06eb3e-c26a-4640-8637-2804246fa927 · outbound

This paper cites an unresolved cited work.

An Augmented Lagrangian Preconditioner for Navier--Stokes Equations with Runge--Kutta in Time Unresolved cited work

Reference 16

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Source-reported events for the cited work

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Observation ed51f891-8327-4749-88d5-3907363103fd · outbound

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An Augmented Lagrangian Preconditioner for Navier--Stokes Equations with Runge--Kutta in Time Unresolved cited work

Reference 17

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Source-reported events for the cited work

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Observation 82363d03-da7f-43e2-9817-22c9b31fb419 · outbound

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An Augmented Lagrangian Preconditioner for Navier--Stokes Equations with Runge--Kutta in Time Unresolved cited work

Reference 18

Resolution
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Source-reported events for the cited work

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Observation 38a1f827-a324-48fc-97b4-b1e9ebc7c6d6 · outbound

This paper cites an unresolved cited work.

An Augmented Lagrangian Preconditioner for Navier--Stokes Equations with Runge--Kutta in Time Unresolved cited work

Reference 19

Resolution
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Source-reported events for the cited work

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Observation 685c69ae-89bb-4a09-b12e-2d449da3a965 · outbound

This paper cites Hairer and G.

An Augmented Lagrangian Preconditioner for Navier--Stokes Equations with Runge--Kutta in Time Hairer and G

Reference 20

Resolution
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Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.

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Observation 959f17b8-7daf-40c8-b33b-3c2716051faa · outbound

This paper cites Huang and J.

An Augmented Lagrangian Preconditioner for Navier--Stokes Equations with Runge--Kutta in Time Huang and J

Reference 21

Resolution
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Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.

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Observation 644967d7-0a01-4e36-a789-1998d4f17e69 · outbound

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An Augmented Lagrangian Preconditioner for Navier--Stokes Equations with Runge--Kutta in Time Unresolved cited work

Reference 22

Resolution
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Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.

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Observation 1e6ae2be-0f8a-4b0a-83f0-98fa52fb3c81 · outbound

This paper cites Johnson and J.

An Augmented Lagrangian Preconditioner for Navier--Stokes Equations with Runge--Kutta in Time Johnson and J

Reference 23

Resolution
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Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.

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Observation e3145aec-6a07-4a9c-b2a4-4e486f8ebabe · outbound

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An Augmented Lagrangian Preconditioner for Navier--Stokes Equations with Runge--Kutta in Time Unresolved cited work

Reference 24

Resolution
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Source-reported events for the cited work

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Observation 3e4965e1-7633-43b1-ae19-56e9367a6645 · outbound

This paper cites Extending Irksome: improvements in automated Runge--Kutta time stepping for finite element methods.

An Augmented Lagrangian Preconditioner for Navier--Stokes Equations with Runge--Kutta in Time Extending Irksome: improvements in automated Runge--Kutta time stepping for finite element methods

Reference 25

Resolution
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Source-reported events for the cited work

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Observation e4c8738e-5e71-41b8-a367-1c11e3717c7e · outbound

This paper cites Improved ParaDiag via low-rank updates and interpolation.

An Augmented Lagrangian Preconditioner for Navier--Stokes Equations with Runge--Kutta in Time Improved ParaDiag via low-rank updates and interpolation

Reference 26

Resolution
verified exact
local_arxiv, observed 2026-08-07T10:50:51.577016Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.

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Observation 418a8062-58a5-4830-803d-263fcf82a08a · outbound

This paper cites an unresolved cited work.

An Augmented Lagrangian Preconditioner for Navier--Stokes Equations with Runge--Kutta in Time Unresolved cited work

Reference 27

Resolution
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Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.

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Observation c337f0f8-037e-4a6f-8fd9-fc6d7469523e · outbound

This paper cites An augmented Lagrangian preconditioner for the control of the Navier--Stokes equations.

An Augmented Lagrangian Preconditioner for Navier--Stokes Equations with Runge--Kutta in Time An augmented Lagrangian preconditioner for the control of the Navier--Stokes equations

Reference 28

Resolution
verified exact
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Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.

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Observation bacc451f-2238-4af0-9f93-362913556e66 · outbound

This paper cites Leveque, L.

An Augmented Lagrangian Preconditioner for Navier--Stokes Equations with Runge--Kutta in Time Leveque, L

Reference 29

Resolution
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Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.

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Observation d81b295e-affe-484c-855c-705ff8d54574 · outbound

This paper cites Mardal, T.

An Augmented Lagrangian Preconditioner for Navier--Stokes Equations with Runge--Kutta in Time Mardal, T

Reference 30

Resolution
verified fuzzy
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Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.

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Observation a8cbb524-be0a-45a3-8870-6393695f1987 · outbound

This paper cites Marion and T.

An Augmented Lagrangian Preconditioner for Navier--Stokes Equations with Runge--Kutta in Time Marion and T

Reference 31

Resolution
verified fuzzy
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Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.

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Observation 60e87497-5a51-4d07-a6a1-15258e5bfca2 · outbound

This paper cites Matthies and L.

An Augmented Lagrangian Preconditioner for Navier--Stokes Equations with Runge--Kutta in Time Matthies and L

Reference 32

Resolution
verified fuzzy
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Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.

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Observation 40fd9974-8673-4445-89b1-a028baba0cc2 · outbound

This paper cites Munch, I.

An Augmented Lagrangian Preconditioner for Navier--Stokes Equations with Runge--Kutta in Time Munch, I

Reference 33

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Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.

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Observation 37671ff5-8660-467b-8cdb-a7f360c81554 · outbound

This paper cites an unresolved cited work.

An Augmented Lagrangian Preconditioner for Navier--Stokes Equations with Runge--Kutta in Time Unresolved cited work

Reference 34

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Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.

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Observation c5c09337-95f2-4500-8ac5-5342cb5d0f45 · outbound

This paper cites an unresolved cited work.

An Augmented Lagrangian Preconditioner for Navier--Stokes Equations with Runge--Kutta in Time Unresolved cited work

Reference 35

Resolution
unresolved
raw_fallback, observed 2026-08-07T10:50:52.583957Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.

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Observation 5c4e9388-8568-42ba-8df4-12ae69d2703b · outbound

This paper cites an unresolved cited work.

An Augmented Lagrangian Preconditioner for Navier--Stokes Equations with Runge--Kutta in Time Unresolved cited work

Reference 36

Resolution
unresolved
raw_fallback, observed 2026-08-07T10:50:52.561935Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.

source=pdf_text observed=2026-08-07T10:50:51.321707Z digest=sha256:cd8d2e34e9c95ca390048fbd39194c07203c31794286b8d7129cf1c7620d0d94

Observation 8f33a39f-4e8c-46b9-85f8-5b506c425ab2 · outbound

This paper cites Rathgeber, D.

An Augmented Lagrangian Preconditioner for Navier--Stokes Equations with Runge--Kutta in Time Rathgeber, D

Reference 37

Resolution
verified fuzzy
raw_fallback, observed 2026-08-07T10:50:52.525477Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.

source=pdf_text observed=2026-08-07T10:50:51.328190Z digest=sha256:19e229fc0bc7a096080c2c9157b6fdeb0820f0ebc919551cad59eb93835dc73e

Observation 5a91a2a9-9ffc-49aa-bfc9-c59d6ff05ade · outbound

This paper cites Rosseel, T.

An Augmented Lagrangian Preconditioner for Navier--Stokes Equations with Runge--Kutta in Time Rosseel, T

Reference 38

Resolution
verified fuzzy
raw_fallback, observed 2026-08-07T10:50:52.495272Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.

source=pdf_text observed=2026-08-07T10:50:51.336745Z digest=sha256:882df5696e63419c2208e3c183161f06e5989be231884d5bddb788a111349ee6

Observation 317203ba-3bb9-4f79-8e9e-a44e0c8a3f8a · outbound

This paper cites Saad, A flexible inner–outer preconditioned GMRES algorithm , SIAM J.

An Augmented Lagrangian Preconditioner for Navier--Stokes Equations with Runge--Kutta in Time Saad, A flexible inner–outer preconditioned GMRES algorithm , SIAM J

Reference 39

Resolution
verified fuzzy
raw_fallback, observed 2026-08-07T10:50:52.468895Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.

source=pdf_text observed=2026-08-07T10:50:51.347147Z digest=sha256:4f97ba43a9915266e46cb317311343c626c3ba8d3b8a7c1e21ee7cd885ee9ed9

Observation a89c681a-afe6-4614-99d1-87dc35a48545 · outbound

This paper cites Saad and M.

An Augmented Lagrangian Preconditioner for Navier--Stokes Equations with Runge--Kutta in Time Saad and M

Reference 40

Resolution
verified fuzzy
raw_fallback, observed 2026-08-07T10:50:52.437307Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.

source=pdf_text observed=2026-08-07T10:50:51.357180Z digest=sha256:47b44a33620c1331882ab57c3e0a8365ed0a2af97c82b30d1be81ce1df563e54

Observation b67a8b6d-8ba8-412f-b4a2-df4fac5505ea · outbound

This paper cites Sch¨ afer, S.

An Augmented Lagrangian Preconditioner for Navier--Stokes Equations with Runge--Kutta in Time Sch¨ afer, S

Reference 41

Resolution
verified fuzzy
raw_fallback, observed 2026-08-07T10:50:52.412791Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.

source=pdf_text observed=2026-08-07T10:50:51.366599Z digest=sha256:928793422b1d895f6b311be39e82c2eb5eb718d91748a4200fafeac1d5327af2

Observation e82e7397-c830-4b21-8e35-1986cfa1fe7c · outbound

This paper cites an unresolved cited work.

An Augmented Lagrangian Preconditioner for Navier--Stokes Equations with Runge--Kutta in Time Unresolved cited work

Reference 42

Resolution
unresolved
raw_fallback, observed 2026-08-07T10:50:52.382567Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.

source=pdf_text observed=2026-08-07T10:50:51.380134Z digest=sha256:55290aff4961ea28169076962c7c0598cb8a2f6223b2e99062d7a0f4f545be7b

Observation bf619c9e-155b-4231-9c3b-4b1782ee19f6 · outbound

This paper cites Silvester and A.

An Augmented Lagrangian Preconditioner for Navier--Stokes Equations with Runge--Kutta in Time Silvester and A

Reference 43

Resolution
verified fuzzy
raw_fallback, observed 2026-08-07T10:50:52.352037Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.

source=pdf_text observed=2026-08-07T10:50:51.387726Z digest=sha256:6903b0eef086e072b6bed1ef22f824183f8dca5b5f97d395b9ef564cf7157d27

Observation 698edb5e-ad4b-4927-908b-fddd796c0d88 · outbound

This paper cites an unresolved cited work.

An Augmented Lagrangian Preconditioner for Navier--Stokes Equations with Runge--Kutta in Time Unresolved cited work

Reference 44

Resolution
unresolved
raw_fallback, observed 2026-08-07T10:50:52.322836Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.

source=pdf_text observed=2026-08-07T10:50:51.395719Z digest=sha256:8cf607b5da905ed3d939f144d2e89d17807b7fcc5c7f8833870b24f4e4e4b7db

Observation 6ae8a096-4501-4dd1-b6ef-c32296167cfa · outbound

This paper cites an unresolved cited work.

An Augmented Lagrangian Preconditioner for Navier--Stokes Equations with Runge--Kutta in Time Unresolved cited work

Reference 45

Resolution
unresolved
raw_fallback, observed 2026-08-07T10:50:52.289304Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.

source=pdf_text observed=2026-08-07T10:50:51.406425Z digest=sha256:bfb0b579629c9604ddd2f8ad2803763e6819dea46b601b3f67f13d987c030f47

Observation 501fa797-3daf-4a10-b941-ffeca56a26a2 · outbound

This paper cites an unresolved cited work.

An Augmented Lagrangian Preconditioner for Navier--Stokes Equations with Runge--Kutta in Time Unresolved cited work

Reference 46

Resolution
unresolved
raw_fallback, observed 2026-08-07T10:50:52.267173Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.

source=pdf_text observed=2026-08-07T10:50:51.416790Z digest=sha256:7305fda666a0f82e75fc81d630aacfa29e526b411896a31d3d8a68f878afacfd

Observation 87a26d51-6353-4bf5-ada1-5e9cddd4b4b0 · outbound

This paper cites Temam, Navier–Stokes equations: theory and numerical analysis , AMS Chelsea Publishing, 1988.

An Augmented Lagrangian Preconditioner for Navier--Stokes Equations with Runge--Kutta in Time Temam, Navier–Stokes equations: theory and numerical analysis , AMS Chelsea Publishing, 1988

Reference 47

Resolution
verified fuzzy
raw_fallback, observed 2026-08-07T10:50:52.235070Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.

source=pdf_text observed=2026-08-07T10:50:51.428876Z digest=sha256:5c6af83f12db65288ecebe37bc4518fe209a0a7fe994240485b861150a4fd1ba

Observation 858f3bae-32d5-4e64-a4b0-84f7d13d8196 · outbound

This paper cites Tobiska and G.

An Augmented Lagrangian Preconditioner for Navier--Stokes Equations with Runge--Kutta in Time Tobiska and G

Reference 48

Resolution
verified fuzzy
raw_fallback, observed 2026-08-07T10:50:52.171285Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.

source=pdf_text observed=2026-08-07T10:50:51.436342Z digest=sha256:b81c292f5ecfea1e1e8b33ab6a4078b0cb545b4d88f393a2f92906a74a9145e1

Observation ce30cc5a-9313-4bac-88dd-210458650547 · outbound

This paper cites Van Lent and S.

An Augmented Lagrangian Preconditioner for Navier--Stokes Equations with Runge--Kutta in Time Van Lent and S

Reference 49

Resolution
verified fuzzy
raw_fallback, observed 2026-08-07T10:50:52.124639Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.

source=pdf_text observed=2026-08-07T10:50:51.445457Z digest=sha256:c0b1a99ceb86838673e4a0f5644b0ce0942dbd676660565873220e41bbb2740f

Observation de803312-8902-49e4-8a6e-c07b9630add6 · outbound

This paper cites Wathen and T.

An Augmented Lagrangian Preconditioner for Navier--Stokes Equations with Runge--Kutta in Time Wathen and T

Reference 50

Resolution
verified fuzzy
raw_fallback, observed 2026-08-07T10:50:52.086455Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.

source=pdf_text observed=2026-08-07T10:50:51.453181Z digest=sha256:8a482ada29025e8001ff90699f89572323e6f43967526b7c1974a4a3dca22420

Observation cdee6007-5797-4207-ae8e-446197cd80b0 · outbound

This paper cites Wathen and D.

An Augmented Lagrangian Preconditioner for Navier--Stokes Equations with Runge--Kutta in Time Wathen and D

Reference 51

Resolution
verified fuzzy
raw_fallback, observed 2026-08-07T10:50:52.002847Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.

source=pdf_text observed=2026-08-07T10:50:51.462230Z digest=sha256:410b8e3d7d18a682502b04b0806933c46af0929daf36ccc0a934955b8b7c1a03

Observation bfe9e69e-6df1-4c41-9a18-e2bb76359a0e · outbound

This paper cites William, Introduction to the numerical analysis of incompressible viscous flows , SIAM, 2008.

An Augmented Lagrangian Preconditioner for Navier--Stokes Equations with Runge--Kutta in Time William, Introduction to the numerical analysis of incompressible viscous flows , SIAM, 2008

Reference 52

Resolution
verified fuzzy
raw_fallback, observed 2026-08-07T10:50:51.843183Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.

source=pdf_text observed=2026-08-07T10:50:51.469072Z digest=sha256:6cd31e524ddc649f9690b9c0370a88533bee4020913e9a3b0e61ba85ee3b7f5c

Pith citing papers

No inbound Pith citation observations are available.