The DOI matches its Crossref record.
A compiler for variational forms
Open accessAbstract
As a key step towards a complete automation of the finite element method, we present a new algorithm for automatic and efficient evaluation of multilinear variational forms. The algorithm has been implemented in the form of a compiler, the FEniCS Form Compiler (FFC). We present benchmark results for a series of standard variational forms, including the incompressible Navier--Stokes equations and linear elasticity. The speedup compared to the standard quadrature-based approach is impressive; in some cases the speedup is as large as a factor of 1000.
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
DOLFIN: Automated finite element computing
Logg, A., & Wells, G. N. (2010) · ACM Transactions on Mathematical Software · doi:10.1145/1731022.1731030 · Cited by 750
Self-citationAlnæs, M. S., Logg, A., Ølgaard, K. B., Rognes, M. E., & Wells, G. N. (2014) · ACM Transactions on Mathematical Software · doi:10.1145/2566630 · Cited by 615
Self-citationA framework for automated PDE-constrained optimisation
Funke, S. W., & Farrell, P. E. (2013) · arXiv · doi:10.48550/arxiv.1302.3894 · Cited by 58
Metadata
- Authors
- Kirby, R. C., & Logg, A.
- Venue
- ACM Transactions on Mathematical Software
- Published
- 2006-09
- Volume
- 32
- Issue
- 3
- Pages
- 417-444
- ISSN
- 0098-3500 (ISSN-L)
- 1557-7295
- OpenAlex
- W2100418324
- Cited by
- 257
- References
- 0
- FWCI
- 11.19
- Type
- journal article
- Language
- en
- Open access
- green
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 compiler for variational forms. https://app.cochat.ai/papers/10.1145/1163641.1163644
- The paper
- Kirby, R. C., & Logg, A. (2006). A compiler for variational forms. ACM Transactions on Mathematical Software. https://doi.org/10.1145/1163641.1163644
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.
