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Unlocking with residual-free bubbles

✍ Scribed by Leopolde P. Franca; Alessandro Russo

Publisher
Elsevier Science
Year
1997
Tongue
English
Weight
283 KB
Volume
142
Category
Article
ISSN
0045-7825

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✦ Synopsis

Residual-free bubbles are derived for the Timoshenko beam problem. Eliminating these bubbles the resulting formulation is form-identical in using the following tricks to the standard variational formulation: (i) one-point reduced integration on the shear energy term; (ii) replace its coefficient l/e' by l/(e* + @i/12)) in each element; (iii) modify consistently the right-hand side. This final formulation is 'legally' obtained in that the Galerkin method enriched with residual-free bubbles is developed using full integration throughout. Furthermore, this method is nodally exact by construction.

📜 SIMILAR VOLUMES

Simulating transient phenomena via resid
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## a b s t r a c t We derive two stabilized methods for transient equations using static condensation of residual-free bubbles. The methods enhance the stability of the Discontinuous Galerkin method.

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Recovering SUPG using Petrov–Galerkin formulations enriched with adjoint residual-free bubbles
✍ L.P. Franca; A. Russo 📂 Article 📅 2000 🏛 Elsevier Science 🌐 English ⚖ 113 KB

We consider conforming Petrov±Galerkin formulations for the advective and advective±diusive equations. For the linear hyperbolic equation, the continuous formulation is set up using dierent spaces and the discretization follows with dierent ``bubble'' enrichments for the test and trial spaces. Bound

Unusual stabilized finite element method
Unusual stabilized finite element methods and residual free bubbles
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An overview of the unusual stabilized ®nite element method and of the standard Galerkin method enriched with residual free bubble functions is presented. For the ®rst method a concrete model problem illustrates its application in advective±diffusive±reactive equations and for the second method it is

Further considerations on residual-free
Further considerations on residual-free bubbles for advective-diffusive equations
✍ F. Brezzi; L.P. Franca; A. Russo 📂 Article 📅 1998 🏛 Elsevier Science 🌐 English ⚖ 649 KB

We further consider the Galerkin method for advective-diffusive equations in two dimensions. The finite dimensional space employed is of piecewise polynomials enriched with residual-free bubbles (RFB). We show that, in general, this method does not coincide with the SUPG method, unless the piecewise