Paper Citation Record · LEDGER

Error analysis of BDF schemes for the evolutionary incompressible Navier--Stokes equations

As of 19 August 2026, this Paper Citation Record lists 22 of 22 outbound references and 4 inbound Pith citation observations for arXiv:2506.16917.

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

pith.paper-citation-record.v1
2506.16917 v1

Coverage vector

measured 22 of 22 reference resolution

Typed states for the displayed outbound observations.

Source: paper_references, paper_reference_links, observed 2026-08-15T19:30:13.646407Z

measured 26 of 26 standing notices

One-hop event checks from named stored sources.

Source: scholarly_work_events, retraction_status_cache, observed 2026-08-19T06:32:44.657259+00:00

measured 4 of 4 inbound itemization

Pith citing papers itemized under the disclosed page cap.

Source: paper_references, paper_reference_links, observed 2026-08-03T17:15:37.060377Z

measured 0 of 1 external citation measurements

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

Source: arxiv_reference, observed 2026-06-30T13:24:40.796490Z

Reference resolution

22 of 22 outbound references displayed

verified exact0
verified fuzzy19
unresolved3
parse uncertain0
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External citation measurements

No source-named external measurement is stored.

Outbound references

Observation fa9352f2-b0c5-4aa0-ae0f-77d339180213 · outbound

This paper cites Adams and John J.

Error analysis of BDF schemes for the evolutionary incompressible Navier--Stokes equations Adams and John J

Reference 1

Resolution: verified fuzzy; raw_fallback, observed 2026-08-15T19:30:13.916500Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.

Observation 89eeda01-eed8-4a54-b7ec-732d90b2d808 · outbound

This paper cites Backward difference formulae: new multipliers and stability properties for parabolic equations.Math.

Error analysis of BDF schemes for the evolutionary incompressible Navier--Stokes equations Backward difference formulae: new multipliers and stability properties for parabolic equations.Math

Reference 2

Resolution: verified fuzzy; raw_fallback, observed 2026-08-15T19:30:13.905690Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.

Observation b1946e39-82a6-4a70-acdb-38980e6f9c43 · outbound

This paper cites Improving the accuracy of the mini- element approximation to navier-stokes equations.IMA J.

Error analysis of BDF schemes for the evolutionary incompressible Navier--Stokes equations Improving the accuracy of the mini- element approximation to navier-stokes equations.IMA J

Reference 3

Resolution: verified fuzzy; raw_fallback, observed 2026-08-15T19:30:13.893950Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.

Observation 16b61522-7803-4b74-84cb-fd6a03f6163d · outbound

This paper cites The postprocessed mixed finite- element method for the Navier-Stokes equations.SIAM J.

Error analysis of BDF schemes for the evolutionary incompressible Navier--Stokes equations The postprocessed mixed finite- element method for the Navier-Stokes equations.SIAM J

Reference 4

Resolution: verified fuzzy; raw_fallback, observed 2026-08-15T19:30:13.882881Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.

Observation 6feb45a2-af63-4a6a-9e48-64b2aba6fe03 · outbound

This paper cites Brenner and L.

Error analysis of BDF schemes for the evolutionary incompressible Navier--Stokes equations Brenner and L

Reference 5

Resolution: unresolved; no resolver link, observed 2026-08-15T19:30:13.586536Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation e57b4541-2917-4526-834e-c3dde78c69ec · outbound

This paper cites Pointwise error estimates for finite element solutions of the Stokes problem.SIAM J.

Error analysis of BDF schemes for the evolutionary incompressible Navier--Stokes equations Pointwise error estimates for finite element solutions of the Stokes problem.SIAM J

Reference 6

Resolution: verified fuzzy; raw_fallback, observed 2026-08-15T19:30:13.864969Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.

Observation 0c67885a-5989-494a-b88c-2e7aa0dedd02 · outbound

This paper cites Ciarlet.The finite element method for elliptic problems.

Error analysis of BDF schemes for the evolutionary incompressible Navier--Stokes equations Ciarlet.The finite element method for elliptic problems

Reference 7

Resolution: verified fuzzy; raw_fallback, observed 2026-08-15T19:30:13.854299Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.

Observation 14b6519b-cdb3-4b54-8a4a-ce2945c384b9 · outbound

This paper cites Contri, B.

Error analysis of BDF schemes for the evolutionary incompressible Navier--Stokes equations Contri, B

Reference 8

Resolution: verified fuzzy; raw_fallback, observed 2026-08-15T19:30:13.843114Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.

Observation 37a6334c-d23d-4679-ae1c-2aef290c789c · outbound

This paper cites Error analysis for a class of methods for stiff non-linear initial value problems.

Error analysis of BDF schemes for the evolutionary incompressible Navier--Stokes equations Error analysis for a class of methods for stiff non-linear initial value problems

Reference 9

Resolution: verified fuzzy; raw_fallback, observed 2026-08-15T19:30:13.831566Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.

Observation 9c07fb84-75cb-4d89-8165-d518e7d548f6 · outbound

This paper cites an unresolved cited work.

Error analysis of BDF schemes for the evolutionary incompressible Navier--Stokes equations Unresolved cited work

Reference 10

Resolution: unresolved; raw_fallback, observed 2026-08-15T19:30:13.820145Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.

Observation 8644ed33-9419-40f0-8dbe-250a0b400e58 · outbound

This paper cites Grad-div stabi- lization for the evolutionary Oseen problem with inf-sup stable finite elements.J.

Error analysis of BDF schemes for the evolutionary incompressible Navier--Stokes equations Grad-div stabi- lization for the evolutionary Oseen problem with inf-sup stable finite elements.J

Reference 11

Resolution: verified fuzzy; raw_fallback, observed 2026-08-15T19:30:13.808088Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.

Observation fc59f4c6-1304-4e99-9833-8224db3b7482 · outbound

This paper cites Analysis of the grad-div stabilization for the time-dependent Navier-Stokes equations with inf-sup stable finite elements.Adv.

Error analysis of BDF schemes for the evolutionary incompressible Navier--Stokes equations Analysis of the grad-div stabilization for the time-dependent Navier-Stokes equations with inf-sup stable finite elements.Adv

Reference 12

Resolution: verified fuzzy; raw_fallback, observed 2026-08-15T19:30:13.796805Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.

Observation eb056374-de8c-4012-b207-64c6dbaf7a3c · outbound

This paper cites Fully discrete approximations to the time-dependent Navier-Stokes equations with a projection method in time and grad-div stabilization.J.

Error analysis of BDF schemes for the evolutionary incompressible Navier--Stokes equations Fully discrete approximations to the time-dependent Navier-Stokes equations with a projection method in time and grad-div stabilization.J

Reference 13

Resolution: verified fuzzy; raw_fallback, observed 2026-08-15T19:30:13.786312Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.

Observation 8c92c60d-2a43-4221-a837-4f01117ab11c · outbound

This paper cites On the convergence order of the finite element error in the kinetic energy for high Reynolds number incompressible flows.

Error analysis of BDF schemes for the evolutionary incompressible Navier--Stokes equations On the convergence order of the finite element error in the kinetic energy for high Reynolds number incompressible flows

Reference 14

Resolution: verified fuzzy; raw_fallback, observed 2026-08-15T19:30:13.775330Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.

Observation 2d7c9050-d3a4-4a42-9f92-fa9ae49e9135 · outbound

This paper cites Robust error bounds for the Navier-Stokes equations using implicit-explicit second-order BDF method with variable steps.IMA J.

Error analysis of BDF schemes for the evolutionary incompressible Navier--Stokes equations Robust error bounds for the Navier-Stokes equations using implicit-explicit second-order BDF method with variable steps.IMA J

Reference 15

Resolution: verified fuzzy; raw_fallback, observed 2026-08-15T19:30:13.763968Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.

Observation 3c2393b0-f7a7-427d-9213-49d7f297f0a6 · outbound

This paper cites Springer-Verlag, Berlin, 1986.

Error analysis of BDF schemes for the evolutionary incompressible Navier--Stokes equations Springer-Verlag, Berlin, 1986

Reference 16

Resolution: verified fuzzy; raw_fallback, observed 2026-08-15T19:30:13.752156Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.

Observation f3791767-62df-47e3-a306-052e740a3eba · outbound

This paper cites Hairer and G.

Error analysis of BDF schemes for the evolutionary incompressible Navier--Stokes equations Hairer and G

Reference 17

Resolution: verified fuzzy; raw_fallback, observed 2026-08-15T19:30:13.740452Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.

Observation 5d1d0ebf-5e41-4f90-a5f3-9ef5368698da · outbound

This paper cites Heywood and Rolf Rannacher.

Error analysis of BDF schemes for the evolutionary incompressible Navier--Stokes equations Heywood and Rolf Rannacher

Reference 18

Resolution: verified fuzzy; raw_fallback, observed 2026-08-15T19:30:13.727879Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.

Observation 3296a1b0-1740-48fd-bbde-d7a226a4225b · outbound

This paper cites Springer, Cham, 2016.

Error analysis of BDF schemes for the evolutionary incompressible Navier--Stokes equations Springer, Cham, 2016

Reference 19

Resolution: verified fuzzy; raw_fallback, observed 2026-08-15T19:30:13.715793Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.

Observation 043badd3-511e-4fa3-9744-8513d026bd89 · outbound

This paper cites an unresolved cited work.

Error analysis of BDF schemes for the evolutionary incompressible Navier--Stokes equations Unresolved cited work

Reference 20

Resolution: unresolved; raw_fallback, observed 2026-08-15T19:30:13.703623Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.

Observation 3dca81f3-ba24-4685-ade2-8a694b5bc893 · outbound

This paper cites Sch¨ afer, S.

Error analysis of BDF schemes for the evolutionary incompressible Navier--Stokes equations Sch¨ afer, S

Reference 21

Resolution: verified fuzzy; raw_fallback, observed 2026-08-15T19:30:13.692247Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.

Observation 65060b28-37ae-432c-975b-0ca0cd6ad9da · outbound

This paper cites Third-order convergence of three-step BDF method for Navier?Stokes equations withH 1 initial data.J.

Error analysis of BDF schemes for the evolutionary incompressible Navier--Stokes equations Third-order convergence of three-step BDF method for Navier?Stokes equations withH 1 initial data.J

Reference 22

Resolution: verified fuzzy; raw_fallback, observed 2026-08-15T19:30:13.680514Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.

Pith citing papers

Observation f449b2f1-a0c0-46d8-a553-66cb337a9fe6 · inbound

Second order reduced model via incremental projection for Navier Stokes cites this paper.

Second order reduced model via incremental projection for Navier Stokes Error analysis of BDF schemes for the evolutionary incompressible Navier--Stokes equations

Reference 4

Resolution: unresolved; no resolver link, observed 2026-08-03T17:15:37.060377Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 040705e8-fe1c-4e39-bf89-c7414b09e11b · inbound

Unconditionally Long-Time Stable Variable-Step Second-Order ETD Schemes for the 2D Periodic Incompressible NSE cites this paper.

Unconditionally Long-Time Stable Variable-Step Second-Order ETD Schemes for the 2D Periodic Incompressible NSE Error analysis of BDF schemes for the evolutionary incompressible Navier--Stokes equations

Reference 17

Resolution: unresolved; no resolver link, observed 2026-08-03T01:20:32.658327Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 3b55c92b-2105-45df-b030-885329e61f86 · inbound

Viscosity in error upper bound for a consistent splitting scheme of the Navier-Stokes equations cites this paper.

Viscosity in error upper bound for a consistent splitting scheme of the Navier-Stokes equations Error analysis of BDF schemes for the evolutionary incompressible Navier--Stokes equations

Reference 16

Resolution: verified exact; arxiv_id, observed 2026-06-30T13:24:40.798110Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.

Observation 408500e2-1e91-45ca-909f-c49b93ce920c · inbound

A spectral-vanishing-viscosity stabilization of a higher-order consistent splitting scheme for the Navier-Stokes equations cites this paper.

A spectral-vanishing-viscosity stabilization of a higher-order consistent splitting scheme for the Navier-Stokes equations Error analysis of BDF schemes for the evolutionary incompressible Navier--Stokes equations

Reference 16

Resolution: unresolved; no resolver link, observed 2026-07-30T14:55:19.298136Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.