The DOI matches its Crossref record; 15 of the 15 references it cites were found in a registry or an index.
Two classes of mixed finite element methods
Open accessAbstract
Finite element methods are presented in an abstract settings for mixed variational formulations. The methods are constructed by adding to the classical Galerkin method various least-squares like terms. The additional terms involve integrals over element interiors, and include mesh-parameter dependent coefficients. The methods are designed to enhance stability. Consistency is achieved in the sense that exact solutions identically satisfy the variational equations. Applied to various problems, simple finite element interpolations are rendered convergent, including convenient equal-order interpolations which are generally unstable within the Galerkin approach. The methods are subdivided into two classes according to the manner in which stability is attained: (1) Circumventing Babuška-Brezzi condition methods. (2) Satisfying Babuška-Brezzi condition methods. Convergence is established for each class of methods. Applications of the first class of methods to Stokes flow and compressible linear elasticity are presented. The second class of methods is applied to compressible and incompressible elasticity problems.
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Cites
The Finite Element Method for Elliptic Problems
(1978) · Studies in Mathematics and Its Applications · doi:10.1016/s0168-2024(08)x7014-6 · Cited by 8,248
The Finite Element Method for Elliptic Problems
Ciarlet, P. G., & Oden, J. T. (1978) · Journal of Applied Mechanics · doi:10.1115/1.3424474 · Cited by 5,508
Brooks, A. N., & Hughes, T. J. R. (1982) · Computer Methods in Applied Mechanics and Engineering · doi:10.1016/0045-7825(82)90071-8 · Cited by 5,332
Self-citationFinite Element Methods for Navier-Stokes Equations: Theory and Algorithms
Girault, V., & Raviart, P.-A. (1986) · CERN Document Server (European Organization for Nuclear Research) · doi:10.1007/978-3-642-61623-5 · Cited by 4,331
Nedelec, J. C. (1980) · Numerische Mathematik · doi:10.1007/bf01396415 · Cited by 3,297
Hughes, T. J. R., Franca, L. P., & Balestra, M. (1986) · Computer Methods in Applied Mechanics and Engineering · doi:10.1016/0045-7825(86)90025-3 · Cited by 1,450
Self-citationConforming and nonconforming finite element methods for solving the stationary Stokes equations I
Crouzeix, M., & Raviart, P.-A. (1973) · Revue française d'automatique informatique recherche opérationnelle. Mathématique · doi:10.1051/m2an/197307r300331 · Cited by 1,393
A numerical solution of the Navier-Stokes equations using the finite element technique
Taylor, C., & Hood, P. (1973) · Computers & Fluids · doi:10.1016/0045-7930(73)90027-3 · Cited by 1,347
Two families of mixed finite elements for second order elliptic problems
Brezzi, F., Douglas, J., & Marini, L. D. (1985) · Numerische Mathematik · doi:10.1007/bf01389710 · Cited by 1,223
Hughes, T. J. R., & Franca, L. P. (1987) · Computer Methods in Applied Mechanics and Engineering · doi:10.1016/0045-7825(87)90184-8 · Cited by 458
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Hughes, T. J. R., Franca, L. P., & Hulbert, G. M. (1989) · Computer Methods in Applied Mechanics and Engineering · doi:10.1016/0045-7825(89)90111-4 · Cited by 1,458
Self-citationStabilized Finite Element Formulations for Incompressible Flow Computations
Tezduyar, T. E. (1991) · Advances in Applied Mechanics · doi:10.1016/s0065-2156(08)70153-4 · Cited by 913
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
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Metadata
- Authors
- Franca, L. P., & Hughes, T. J. R.
- Venue
- Computer Methods in Applied Mechanics and Engineering
- Publisher
- Elsevier BV
- Published
- 1988-07
- Volume
- 69
- Issue
- 1
- Pages
- 89-129
- ISSN
- 0045-7825 (ISSN-L)
- OpenAlex
- W2061423965
- Cited by
- 305
- References
- 15
- FWCI
- 9.14
- Type
- journal article
- Language
- en
- Open access
- hybrid
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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.
