A posteriori existence for the Keller-Segel model via a finite volume - finite element scheme | Paper Citation Record

Observation 93715f13-d0fc-4b5c-83cb-bd04e458b370 · outbound

This paper cites An unconditionally energy stable and positive upwind DG scheme for the Keller–Segel model.

A posteriori existence for the Keller-Segel model via a finite volume - finite element scheme An unconditionally energy stable and positive upwind DG scheme for the Keller–Segel model

Reference 1

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Observation 136eea1d-9a35-4e7d-842c-269c212c47fc · outbound

This paper cites Two and three dimensional H2-conforming finite element approximations without C1-elements.

A posteriori existence for the Keller-Segel model via a finite volume - finite element scheme Two and three dimensional H2-conforming finite element approximations without C1-elements

Reference 2

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Observation cc6aeaac-43d4-4acd-81ae-56ff7ad864d7 · outbound

This paper cites Bartels.Numerical methods for nonlinear partial differential equations.

A posteriori existence for the Keller-Segel model via a finite volume - finite element scheme Bartels.Numerical methods for nonlinear partial differential equations

Reference 3

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Observation 7e5e0377-8318-419f-9688-81d5324e7e62 · outbound

This paper cites Bartels.Numerical methods for partial differential equations.

A posteriori existence for the Keller-Segel model via a finite volume - finite element scheme Bartels.Numerical methods for partial differential equations

Reference 4

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Observation 2e9fdb9b-5f93-4557-a10c-e736e87e33d6 · outbound

This paper cites Robust a priori and a posteriori error analysis for the approximation of Allen–Cahn and Ginzburg–Landau equations past topologi- cal changes.

A posteriori existence for the Keller-Segel model via a finite volume - finite element scheme Robust a priori and a posteriori error analysis for the approximation of Allen–Cahn and Ginzburg–Landau equations past topologi- cal changes

Reference 5

Resolution: verified exact; doi, observed 2026-08-15T15:55:25.858940Z

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Observation d36ab1e6-3275-4de2-8d63-be1b73fc7da9 · outbound

This paper cites A note on the Poincar´ e inequality for convex domains.

A posteriori existence for the Keller-Segel model via a finite volume - finite element scheme A note on the Poincar´ e inequality for convex domains

Reference 6

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Observation 3649bb82-0aa9-4dc0-8a97-7684f58d1991 · outbound

This paper cites A finite volume scheme for convection–diffusion equations with nonlinear diffusion derived from the Scharfetter–Gummel scheme.

A posteriori existence for the Keller-Segel model via a finite volume - finite element scheme A finite volume scheme for convection–diffusion equations with nonlinear diffusion derived from the Scharfetter–Gummel scheme

Reference 7

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Observation fe1efe1a-ca7e-468b-8455-ec0fea7c6039 · outbound

This paper cites Local and global solvability of some parabolic systems modelling chemotaxis.

A posteriori existence for the Keller-Segel model via a finite volume - finite element scheme Local and global solvability of some parabolic systems modelling chemotaxis

Reference 8

Resolution: verified fuzzy; raw_fallback, observed 2026-08-15T15:55:26.081569Z

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Observation cd618f93-70c8-4554-96bf-4be14d446582 · outbound

This paper cites Existence and nonexistence of solutions for a model of grav- itational interaction of particles, I.

A posteriori existence for the Keller-Segel model via a finite volume - finite element scheme Existence and nonexistence of solutions for a model of grav- itational interaction of particles, I

Reference 9

Resolution: verified exact; doi, observed 2026-08-15T15:55:25.838449Z

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Observation 8fcdaee8-188d-4822-8829-4b88646635c5 · outbound

This paper cites an unresolved cited work.

A posteriori existence for the Keller-Segel model via a finite volume - finite element scheme Unresolved cited work

Reference 10

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Observation 8b124fcb-f99b-4ba8-ad77-73baf1b47a41 · outbound

This paper cites A Posteriori Error Control for the Allen–Cahn Equation with Variable Mobility.

A posteriori existence for the Keller-Segel model via a finite volume - finite element scheme A Posteriori Error Control for the Allen–Cahn Equation with Variable Mobility

Reference 11

Resolution: verified exact; doi, observed 2026-08-15T15:55:25.822888Z

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Observation 193d36f9-f5c4-4a3f-8eae-6cf38e56ffe3 · outbound

This paper cites Brunk, J.

A posteriori existence for the Keller-Segel model via a finite volume - finite element scheme Brunk, J

Reference 12

Resolution: verified fuzzy; raw_fallback, observed 2026-08-15T15:55:26.072993Z

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Observation 2b3de7f6-8257-45bc-9546-02e4619bea14 · outbound

This paper cites A numerical verification method for a system of FitzHugh-Nagumo type.

A posteriori existence for the Keller-Segel model via a finite volume - finite element scheme A numerical verification method for a system of FitzHugh-Nagumo type

Reference 13

Resolution: verified exact; raw_fallback, observed 2026-08-15T15:55:25.997414Z

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Observation 1931a99b-7331-47a2-84d0-c9ad607cf547 · outbound

This paper cites Adaptivity and blow-up detection for nonlinear evolution problems.

A posteriori existence for the Keller-Segel model via a finite volume - finite element scheme Adaptivity and blow-up detection for nonlinear evolution problems

Reference 14

Resolution: verified exact; doi, observed 2026-08-15T15:55:25.813202Z

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Observation 3849e8ae-3d07-442e-b009-3d44397f4bca · outbound

This paper cites A posteriori error estimates for un- steady convection–diffusion–reaction problems and the finite volume method.

A posteriori existence for the Keller-Segel model via a finite volume - finite element scheme A posteriori error estimates for un- steady convection–diffusion–reaction problems and the finite volume method

Reference 15

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Observation 5ebbf6f4-8821-4d36-a612-900bc5779a0a · outbound

This paper cites Error estimates and blow-up analysis of a finite-element approximation for the parabolic-elliptic Keller-Segel system.

A posteriori existence for the Keller-Segel model via a finite volume - finite element scheme Error estimates and blow-up analysis of a finite-element approximation for the parabolic-elliptic Keller-Segel system

Reference 16

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Observation dee10397-cb85-4121-9ca9-97d74953e9ba · outbound

This paper cites A second-order positivity preserving central-upwind scheme for chemotaxis and haptotaxis models.

A posteriori existence for the Keller-Segel model via a finite volume - finite element scheme A second-order positivity preserving central-upwind scheme for chemotaxis and haptotaxis models

Reference 17

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Observation d51baac6-896b-462c-a0f0-990bab47ff18 · outbound

This paper cites Convergence rate of a finite volume schemefor a two dimensional convection-diffusion problem.

A posteriori existence for the Keller-Segel model via a finite volume - finite element scheme Convergence rate of a finite volume schemefor a two dimensional convection-diffusion problem

Reference 18

Resolution: malformed identifier; raw_fallback, observed 2026-08-15T15:55:26.064369Z

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Observation 5348f744-5c91-47b8-b40c-9b559c9d2b56 · outbound

This paper cites Maximum-norm a posteriori error estimates for singu- larly perturbed elliptic reaction-diffusion problems.

A posteriori existence for the Keller-Segel model via a finite volume - finite element scheme Maximum-norm a posteriori error estimates for singu- larly perturbed elliptic reaction-diffusion problems

Reference 19

Resolution: verified exact; doi, observed 2026-08-15T15:55:25.785510Z

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Observation 7d0d47fd-d544-4f9d-883c-a958e25f2788 · outbound

This paper cites an unresolved cited work.

A posteriori existence for the Keller-Segel model via a finite volume - finite element scheme Unresolved cited work

Reference 20

Resolution: unresolved; raw_fallback, observed 2026-08-15T15:55:26.055151Z

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Observation a9582964-63e9-40c5-a239-9b37a23a878c · outbound

This paper cites Green’s matrices of second order elliptic systems with measurable coefficients in two dimensional domains.

A posteriori existence for the Keller-Segel model via a finite volume - finite element scheme Green’s matrices of second order elliptic systems with measurable coefficients in two dimensional domains

Reference 21

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Observation 13df14a3-a4b0-4e35-b394-2651b5fb72e2 · outbound

This paper cites Fully discrete analysis of a discontinuous finite element method for the Keller-Segel chemotaxis model.

A posteriori existence for the Keller-Segel model via a finite volume - finite element scheme Fully discrete analysis of a discontinuous finite element method for the Keller-Segel chemotaxis model

Reference 22

Resolution: verified exact; doi, observed 2026-08-15T15:55:25.771305Z

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Observation 2403944f-7ca5-4d5e-a2ac-34463977cb98 · outbound

This paper cites New interior penalty discontinuous Galerkin methods for the Keller–Segel chemotaxis model.

A posteriori existence for the Keller-Segel model via a finite volume - finite element scheme New interior penalty discontinuous Galerkin methods for the Keller–Segel chemotaxis model

Reference 23

Resolution: verified exact; doi, observed 2026-08-15T15:55:25.762896Z

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Observation 93daf45b-ae0b-4551-be0f-9f0a44712dba · outbound

This paper cites A posteriori error estimation based on potential and flux reconstruction for the heat equation.

A posteriori existence for the Keller-Segel model via a finite volume - finite element scheme A posteriori error estimation based on potential and flux reconstruction for the heat equation

Reference 24

Resolution: verified exact; doi, observed 2026-08-15T15:55:25.754638Z

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Observation cb4048d9-f7dd-44e7-9c6e-8231ed25343e · outbound

This paper cites Estimates for the Sobolev trace constant with critical exponent and applications.

A posteriori existence for the Keller-Segel model via a finite volume - finite element scheme Estimates for the Sobolev trace constant with critical exponent and applications

Reference 25

Resolution: verified exact; doi, observed 2026-08-15T15:55:25.745779Z

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Observation ed2b9b42-0f4c-43ea-819a-8fa607a413f5 · outbound

This paper cites A finite volume scheme for the Patlak–Keller–Segel chemotaxis model.

A posteriori existence for the Keller-Segel model via a finite volume - finite element scheme A finite volume scheme for the Patlak–Keller–Segel chemotaxis model

Reference 26

Resolution: malformed identifier; raw_fallback, observed 2026-08-15T15:55:26.046120Z

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Observation bdad95ef-cf5a-4d48-a28a-d86e6c79a72b · outbound

This paper cites A posteriori error analysis of a positivity preserving scheme for the power-law diffusion Keller–Segel model.

A posteriori existence for the Keller-Segel model via a finite volume - finite element scheme A posteriori error analysis of a positivity preserving scheme for the power-law diffusion Keller–Segel model

Reference 27

Resolution: verified exact; doi, observed 2026-08-15T15:55:25.737355Z

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Observation 73bcbb01-2484-4b14-9636-a6ce9fa24d05 · outbound

This paper cites A posteriori error control for a discontinuous Galerkin approximation of a Keller-Segel model.

A posteriori existence for the Keller-Segel model via a finite volume - finite element scheme A posteriori error control for a discontinuous Galerkin approximation of a Keller-Segel model

Reference 28

Resolution: verified exact; doi, observed 2026-08-15T15:55:25.728493Z

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Observation b55f8b2e-433f-475c-8408-56122a1aaf71 · outbound

This paper cites Grisvard.Elliptic Problems in Nonsmooth Domains.

A posteriori existence for the Keller-Segel model via a finite volume - finite element scheme Grisvard.Elliptic Problems in Nonsmooth Domains

Reference 29

Resolution: verified fuzzy; raw_fallback, observed 2026-08-15T15:55:26.037012Z

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Observation 49731658-343f-4303-824d-c41f3137ed1c · outbound

This paper cites Energy dissipative local discontinuous Galerkin methods for Keller–Segel chemotaxis model.

A posteriori existence for the Keller-Segel model via a finite volume - finite element scheme Energy dissipative local discontinuous Galerkin methods for Keller–Segel chemotaxis model

Reference 30

Resolution: verified exact; doi, observed 2026-08-15T15:55:25.719574Z

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Observation 634c07d9-a8e4-4c1d-8558-4a4044a0eb8a · outbound

This paper cites Exact sequences on Worsey–Farin splits.

A posteriori existence for the Keller-Segel model via a finite volume - finite element scheme Exact sequences on Worsey–Farin splits

Reference 31

Resolution: verified exact; doi, observed 2026-08-15T15:55:25.710897Z

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Observation 0bd52688-3be3-45b0-a0d2-30f1ce6b6dfa · outbound

This paper cites TetGen, a Delaunay-based quality tetrahedral mesh generator.

A posteriori existence for the Keller-Segel model via a finite volume - finite element scheme TetGen, a Delaunay-based quality tetrahedral mesh generator

Reference 32

Resolution: unresolved; no resolver link, observed 2026-08-15T15:55:25.428159Z

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Observation 4b87c041-0ecd-45c2-b19e-9105b0f5bb87 · outbound

This paper cites Efficient Numerical Schemes for a Two-Species Keller-Segel Model and Investigation of Its Blowup Phenomena in 3D.

A posteriori existence for the Keller-Segel model via a finite volume - finite element scheme Efficient Numerical Schemes for a Two-Species Keller-Segel Model and Investigation of Its Blowup Phenomena in 3D

Reference 33

Resolution: verified exact; doi, observed 2026-08-15T15:55:25.696002Z

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Observation c0cebe0a-1973-40b5-ba21-630f7d056362 · outbound

This paper cites A discrete boundedness-by-entropy method for finite-volume approximations of cross-diffusion systems.

A posteriori existence for the Keller-Segel model via a finite volume - finite element scheme A discrete boundedness-by-entropy method for finite-volume approximations of cross-diffusion systems

Reference 34

Resolution: verified exact; doi, observed 2026-08-15T15:55:25.686140Z

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Observation a44c7297-80fb-45e8-94de-9ede4e200756 · outbound

This paper cites Initiation of slime mold aggregation viewed as an in- stability.

A posteriori existence for the Keller-Segel model via a finite volume - finite element scheme Initiation of slime mold aggregation viewed as an in- stability

Reference 35

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Observation d789dfe0-c384-498f-a487-20a57405d7f1 · outbound

This paper cites A general approach to transforming finite elements.

A posteriori existence for the Keller-Segel model via a finite volume - finite element scheme A general approach to transforming finite elements

Reference 36

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Observation e50c5094-e204-4c20-89f4-eecbf77d1fe1 · outbound

This paper cites Analysis for time discrete approximations of blow-up solu- tions of semilinear parabolic equations.

A posteriori existence for the Keller-Segel model via a finite volume - finite element scheme Analysis for time discrete approximations of blow-up solu- tions of semilinear parabolic equations

Reference 37

Resolution: verified exact; doi, observed 2026-08-15T15:55:25.666549Z

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Observation 1138cc62-dd12-4f16-a453-4ac97a0a14ac · outbound

This paper cites Pointwise a posteriori error bounds for blow-up in the semi- linear heat equation.

A posteriori existence for the Keller-Segel model via a finite volume - finite element scheme Pointwise a posteriori error bounds for blow-up in the semi- linear heat equation

Reference 38

Resolution: verified exact; doi, observed 2026-08-15T15:55:25.657318Z

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Observation 5ca29ec0-1f3b-4cbf-9e0c-953536471555 · outbound

This paper cites Local discontinuous Galerkin method for the Keller- Segel chemotaxis model.

A posteriori existence for the Keller-Segel model via a finite volume - finite element scheme Local discontinuous Galerkin method for the Keller- Segel chemotaxis model

Reference 39

Resolution: verified exact; doi, observed 2026-08-15T15:55:25.647888Z

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Observation 8f2f8c11-394e-4380-954f-c54b7f987cd4 · outbound

This paper cites Space and time reconstructions in a posteriori analysis of evolution problems.

A posteriori existence for the Keller-Segel model via a finite volume - finite element scheme Space and time reconstructions in a posteriori analysis of evolution problems

Reference 40

Resolution: verified exact; doi, observed 2026-08-15T15:55:25.638372Z

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Observation a7988551-1938-4d24-8dd5-162b21cefdd8 · outbound

This paper cites Elliptic reconstruction and a posteriori error esti- mates for parabolic problems.

A posteriori existence for the Keller-Segel model via a finite volume - finite element scheme Elliptic reconstruction and a posteriori error esti- mates for parabolic problems

Reference 41

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Observation f7222ba5-3308-4f8f-b45c-9f0a5e63c012 · outbound

This paper cites Solutions of the 3D Navier–Stokes equations for initial data in ˙H1/2: robustness of regularity and numerical verification of regularity for bounded sets of initial data in ˙H1.

A posteriori existence for the Keller-Segel model via a finite volume - finite element scheme Solutions of the 3D Navier–Stokes equations for initial data in ˙H1/2: robustness of regularity and numerical verification of regularity for bounded sets of initial data in ˙H1

Reference 42

Resolution: malformed identifier; no resolver link, observed 2026-08-15T15:55:25.463688Z

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Observation 95c71cd7-de92-4dfb-a8ab-ea59a01a59ac · outbound

This paper cites A method of verified computa- tions for solutions to semilinear parabolic equations using semigroup theory.

A posteriori existence for the Keller-Segel model via a finite volume - finite element scheme A method of verified computa- tions for solutions to semilinear parabolic equations using semigroup theory

Reference 43

Resolution: verified fuzzy; raw_fallback, observed 2026-08-15T15:55:26.028004Z

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Observation 00468c90-c621-445a-9329-a2a7b7143177 · outbound

This paper cites Estimation of Sobolev embedding constant on a domain dividable into bounded convex domains.

A posteriori existence for the Keller-Segel model via a finite volume - finite element scheme Estimation of Sobolev embedding constant on a domain dividable into bounded convex domains

Reference 44

Resolution: malformed identifier; doi_truncated, observed 2026-08-15T15:55:25.619187Z

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Observation e5a49e3e-a43e-4ada-a12d-28b400f5b822 · outbound

This paper cites On approximate solutions of the incompressible Euler and Navier–Stokes equations.

A posteriori existence for the Keller-Segel model via a finite volume - finite element scheme On approximate solutions of the incompressible Euler and Navier–Stokes equations

Reference 45

Resolution: verified exact; doi, observed 2026-08-15T15:55:25.609878Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.

Observation 5b91825a-b211-4887-ae6e-1b45675151ae · outbound

This paper cites Behavior of radially symmetric solutions of a system related to chemotaxis.

A posteriori existence for the Keller-Segel model via a finite volume - finite element scheme Behavior of radially symmetric solutions of a system related to chemotaxis

Reference 46

Resolution: verified exact; doi, observed 2026-08-15T15:55:25.600491Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.

Observation 6bbe2041-7d65-41b6-8ef3-477a83193b63 · outbound

This paper cites A Posteriori Error Estimations of Some Cell Centered Finite Volume Meth- ods for Diffusion-Convection-Reaction Problems.

A posteriori existence for the Keller-Segel model via a finite volume - finite element scheme A Posteriori Error Estimations of Some Cell Centered Finite Volume Meth- ods for Diffusion-Convection-Reaction Problems

Reference 47

Resolution: verified exact; doi, observed 2026-08-15T15:55:25.591112Z

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Observation ba6e6a73-77b6-4f7a-8f6d-56e1776f5df3 · outbound

This paper cites A posteriori existence in numerical computations.

A posteriori existence for the Keller-Segel model via a finite volume - finite element scheme A posteriori existence in numerical computations

Reference 48

Resolution: verified fuzzy; raw_fallback, observed 2026-08-15T15:55:26.018009Z

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Observation efcc5d89-dece-4de8-867e-f9802307c954 · outbound

This paper cites A mixed finite element method for 2-nd order elliptic problems.

A posteriori existence for the Keller-Segel model via a finite volume - finite element scheme A mixed finite element method for 2-nd order elliptic problems

Reference 49

Resolution: unresolved; no resolver link, observed 2026-08-15T15:55:25.485790Z

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Observation 5e228d0a-c145-4391-ba17-eb730c14eb1a · outbound

This paper cites Conservative upwind finite-element method for a simplified Keller–Segel sys- tem modelling chemotaxis.

A posteriori existence for the Keller-Segel model via a finite volume - finite element scheme Conservative upwind finite-element method for a simplified Keller–Segel sys- tem modelling chemotaxis

Reference 50

Resolution: verified exact; doi, observed 2026-08-15T15:55:25.575103Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.

Observation 2cdc6af5-7960-4be8-9948-fe7ed00bc3d3 · outbound

This paper cites A positivity-preserving finite element method for chemotaxis problems in 3D.

A posteriori existence for the Keller-Segel model via a finite volume - finite element scheme A positivity-preserving finite element method for chemotaxis problems in 3D

Reference 51

Resolution: malformed identifier; raw_fallback, observed 2026-08-15T15:55:26.006911Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.

Observation d737215e-c3ab-4de5-af86-4b93987de1da · outbound

This paper cites A positivity preserving moving mesh finite element method for the Keller–Segel chemotaxis model.

A posteriori existence for the Keller-Segel model via a finite volume - finite element scheme A positivity preserving moving mesh finite element method for the Keller–Segel chemotaxis model

Reference 52

Resolution: verified exact; doi, observed 2026-08-15T15:55:25.565852Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.

Observation d67ebc45-79e4-4641-be92-a3e1b4b8f9bb · outbound

This paper cites Triangulation of simple 3D shapes with well-centered tetrahedra.

A posteriori existence for the Keller-Segel model via a finite volume - finite element scheme Triangulation of simple 3D shapes with well-centered tetrahedra

Reference 53

Resolution: verified exact; doi, observed 2026-08-15T15:55:25.556815Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.

Observation 1a8b9eab-3ded-42cb-9b9f-fca536c6b8e5 · outbound

This paper cites Verf¨ urth.A posteriori error estimation techniques for finite element methods.

A posteriori existence for the Keller-Segel model via a finite volume - finite element scheme Verf¨ urth.A posteriori error estimation techniques for finite element methods

Reference 54

Resolution: unresolved; no resolver link, observed 2026-08-15T15:55:25.501767Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 32e26957-ca5d-470e-86cb-4044e16c9647 · outbound

This paper cites Error estimates for somequasi-interpolation operators.

A posteriori existence for the Keller-Segel model via a finite volume - finite element scheme Error estimates for somequasi-interpolation operators

Reference 55

Resolution: verified exact; doi, observed 2026-08-15T15:55:25.547557Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.

Observation 67599b0b-72fe-431e-a87a-f2dec9ef03a7 · outbound

This paper cites Modeling chemotactic waves in saturated porous media using adaptive mesh refinement.

A posteriori existence for the Keller-Segel model via a finite volume - finite element scheme Modeling chemotactic waves in saturated porous media using adaptive mesh refinement

Reference 56

Resolution: verified exact; doi, observed 2026-08-15T15:55:25.538170Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.

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