| Full text | |
| Author(s): |
Avila da Silva, Jr., C. R.
[1]
;
Beck, Andre Teofilo
[2]
;
Franco, Admilson T.
[1]
;
de Suarez, Oscar A.
[3]
Total Authors: 4
|
| Affiliation: | [1] Fed Technol Univ Parana, Dept Mech Engn, BR-80230901 Curitiba, Parana - Brazil
[2] Univ Sao Paulo, Dept Struct Engn, BR-13566590 Sao Carlos, SP - Brazil
[3] Univ Caxias, Dept Mech Engn, BR-95070560 Caxias Do Sul, RS - Brazil
Total Affiliations: 3
|
| Document type: | Journal article |
| Source: | JOURNAL OF HEAT TRANSFER-TRANSACTIONS OF THE ASME; v. 135, n. 7 JUL 2013. |
| Web of Science Citations: | 0 |
| Abstract | |
In this paper, the Galerkin method is used to obtain numerical solutions to two-dimensional steady-state reaction-diffusion problems. Uncertainties in reaction and diffusion coefficients are modeled using parameterized stochastic processes. A stochastic version of the Lax-Milgram lemma is used in order to guarantee existence and uniqueness of the theoretical solutions. The space of approximate solutions is constructed by tensor product between finite dimensional deterministic functional spaces and spaces generated by chaos polynomials, derived from the Askey-Wiener scheme. Performance of the developed Galerkin scheme is evaluated by comparing first and second order moments and probability histograms obtained from approximate solutions with the corresponding estimates obtained via Monte Carlo simulation. Results for three example problems show very fast convergence of the approximate Galerkin solutions. Results also show that complete probability densities (histograms) of the responses are correctly approximated by the developed Galerkin basis. (AU) | |
| FAPESP's process: | 08/10366-4 - Claudio Roberto Ávila da Silva Junior | Universidade Tecnológica Federal do Paraná - campus Curitiba - Brazil |
| Grantee: | André Teófilo Beck |
| Support Opportunities: | Research Grants - Visiting Researcher Grant - Brazil |