| Full text | |
| Author(s): |
Remy Bernard Devloo, Philippe
[1]
;
Duran, Omar
[1]
;
Monteiro Farias, Agnaldo
[2]
;
Maria Gomes, Sonia
[3]
Total Authors: 4
|
| Affiliation: | [1] Univ Estadual Campinas, FEC, Campinas - Brazil
[2] IFNMG, Dept Matemat, Salinas - Brazil
[3] Univ Estadual Campinas, IMECC, Campinas - Brazil
Total Affiliations: 3
|
| Document type: | Journal article |
| Source: | INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING; v. 121, n. 13 MAR 2020. |
| Web of Science Citations: | 0 |
| Abstract | |
Effects of nonaffine elements on the accuracy of 3D H(div)-conforming finite elements are studied. Instead of convergence order k+1 for the flux and the divergence of the flux obtained with Raviart-Thomas or Nedelec spaces with normal traces of degree k, based on affine hexahedra or triangular prisms, reduced orders k for the flux and k-1 for the divergence of the flux may occur for distorted elements. To improve this scenario, a hierarchy of enriched flux approximations is considered, by adding internal shape functions up to a higher degree k+n, n>0, while keeping the original normal traces of degree k. The resulting enriched approximations, using multilinear transformations, keep the original flux accuracy (of order k+1 with affine elements or reduced order k otherwise), but enhanced divergence (of order k+n+1, in the affine case, or k+n-1 otherwise) can be reached. The reduced flux accuracy due to quadrilateral face distortions cannot be corrected by including higher order internal functions. The enriched spaces are applied to the mixed finite element formulation of Darcy's model. The computational cost of matrix assembly increases with n, but the condensed system to be solved has the same dimension and structure as the original scheme. (AU) | |
| FAPESP's process: | 16/13637-5 - Advanced numerical methods: recent developments, analysis, and applications |
| Grantee: | Sônia Maria Gomes |
| Support Opportunities: | Research Grants - Meeting - Abroad |