The DOI matches its Crossref record.
A new finite element formulation for computational fluid dynamics: V. Circumventing the babuška-brezzi condition: a stable Petrov-Galerkin formulation of the stokes problem accommodating equal-order interpolations
Open accessAbstract
A new Petrov-Galerkin formulation of the Stokes problem is proposed. The new formulation possesses better stability properties than the classical Galerkin/variational method. An error analysis is performed for the case in which both the velocity and pressure are approximated by C0 interpolations. Combinations of C0 interpolations which are unstable according to the Babuška-Brezzi condition (e.g., equal-order interpolations) are shown to be stable and convergent within the present framework. Calculations exhibiting the good behavior of the methodology are presented.
Overview
The claims and statistics of this paper haven’t been checked yet.
Run the check — free, no account needed. It reads the open-access text and checks the sources it cites.
Integrity signals
Registry
Cites
Statistics
Verification
Claims the paper makes
The claims and statistics of this paper haven’t been checked yet.
Run the check — free, no account needed. It reads the open-access text and checks the sources it cites.
Self-check
Percentages, sums and reported differences re-computed from the paper’s own numbers.
The self-check needs the paper’s full text.
Citations
Cited by
Finite element modeling of blood flow in arteries
Taylor, C. A., Hughes, T. J. R., & Zarins, C. K. (1998) · Computer Methods in Applied Mechanics and Engineering · doi:10.1016/s0045-7825(98)80008-x · Cited by 726
Self-citationTHE PARTICLE FINITE ELEMENT METHOD — AN OVERVIEW
OÑATE, E., IDELSOHN, S. R., DEL PIN, F., & AUBRY, R. (2004) · International Journal of Computational Methods · doi:10.1142/s0219876204000204 · Cited by 538
Finite element methods for flow problems with moving boundaries and interfaces
Tezduyar, T. E. (2001) · Archives of Computational Methods in Engineering · doi:10.1007/bf02897870 · Cited by 386
Stabilized Finite Element Methods
Franca, L. P., Hughes, T. J. R., & Stenberg, R. (1993) · Incompressible Computational Fluid Dynamics · doi:10.1017/cbo9780511574856.005 · Cited by 328
Self-citationEighty Years of the Finite Element Method: Birth, Evolution, and Future
Liu, W. K., Li, S., & Park, H. S. (2022) · Archives of Computational Methods in Engineering · doi:10.1007/s11831-022-09740-9 · Cited by 322
Metadata
- Authors
- Hughes, T. J. R., Franca, L. P., & Balestra, M.
- Venue
- Computer Methods in Applied Mechanics and Engineering
- Publisher
- Elsevier BV
- Published
- 1986-11
- Volume
- 59
- Issue
- 1
- Pages
- 85-99
- ISSN
- 0045-7825 (ISSN-L)
- OpenAlex
- W1986608219
- Cited by
- 1,450
- References
- 0
- FWCI
- 11.20
- Type
- journal article
- Language
- en
- Open access
- hybrid
About these checks
Registry, retraction, Cites and statistics results are computed, not judged, with one exception: a printed reference that no index lists is read once by a model before it counts as a citation error. Claims are extracted by a model and kept only when their quote appears verbatim in the text; each cited source is then checked, with a model’s help, for whether it says what the claim relies on. Those verdicts can be wrong — read the claim’s quote and the cited source before relying on one.
Statistics and arithmetic are recomputed, not judged.
Confidence bands are shown only for fields calibrated on our annotated test set. None is calibrated yet, so no band is shown.
What counts as a claim ›How we measure confidence ›How we check this ›
Are you an author, or do you see a problem with this page? Request a review
How to cite
Cite CoChat for the checks on this page, and the paper for its own findings.
- This page
- CoChat. (2026). Citation check: A new finite element formulation for computational fluid dynamics: V. Circumventing the babuška-brezzi condition: a stable Petrov-Galerkin formulation of the stokes problem accommodating equal-order interpolations. https://app.cochat.ai/papers/10.1016/0045-7825(86)90025-3
- The paper
- Hughes, T. J. R., Franca, L. P., & Balestra, M. (1986). A new finite element formulation for computational fluid dynamics: V. Circumventing the babuška-brezzi condition: a stable Petrov-Galerkin formulation of the stokes problem accommodating equal-order interpolations. Computer Methods in Applied Mechanics and Engineering. https://doi.org/10.1016/0045-7825(86)90025-3
Data sources
Bibliographic data: Semantic Scholar, OpenAlex, Crossref.
Contains information from the Semantic Scholar Academic Graph Datasets, made available under the ODC Attribution License (ODC-BY 1.0).
Semantic Scholar’s data is described in: Kinney, R., et al. (2023). The Semantic Scholar Open Data Platform. arXiv:2301.10140.
