• Philippe R. B. Devloo Universidade Estadual de Campinas
  • Omar Durán Universidade Estadual de Campinas
  • Sônia M. Gomes Universidade Estadual de Campinas
  • Nathan Shauer Civil & Environmental Engineering, University of Illinois Urbana-Champaign, USA




Mixed finite elements. H(div)-conforming spaces. Curved elements. Hp-adaptivity.


Two stable approximation space configurations are treated for discrete versions of the mixed finite element method for elliptic problems. The construction of these approximation spaces are based on curved 3D meshes composed of different topologies (tetrahedral, hexahedral or prismatic elements). Furthermore, their choices are guided by the property that, in the master element, the image of the flux space by the divergence operator coincides with the primal space. Additionally, by using static condensation, the global condensed matrices sizes, which are proportional to the dimension of border fluxes, are reduced, noting that this dimension is the same in both configurations. For uniform meshes with constant polynomial degree distribution, accuracy of order k + 1 or k + 2 for the primal variable is reached, while keeping order k + 1 for the flux in both configurations. The case of hp-adaptive meshes is treated for application to the simulation of the flow in a porous media around a cylindrical well. The effect of parallelism and static condensation in CPU time reduction is illustrated.


Não há dados estatísticos.


Brezzi, F., Douglas, J., Fortin, &Marini, L. D., 1987. Efficient rectangular mixed finite elements in two and three space variable, RAIRO Mod´el. Math. Anal. Num´er. vol. 2, pp. 581”“604.

Brezzi, F., & Fortin, M., 1991. Mixed and Hybrid Finite Element Methods, Springer Series in Computational Mathematics, vol. 15, Springer-Verlag, NewYork.

Calle, J. L. D., Devloo, P. R. B., & Gomes, S. M., 2015. Implementation of continuous hp-adaptive finite element spaces without limitations on hanging sides and distribution of approximation orders. Compt. & Math. Appl. vol. 70, n. 5, pp. 1051”“1069.

Castro, D. A., Devloo, P. R. B., Farias, A. M., Gomes, S. M., Siqueira D., & Dur´an, O., 2016a. Three dimensional hierarchical mixed finite element approximations with enhanced primal variable accuracy. Comput. Meth. Appl. Mech. Eng. v. 306, pp. 479”“502.

Castro, D. A., Devloo, P. R. B., Farias, A. M., Gomes, S. M., & Dur´an, O., 2016b. Hierarchical high order finite element bases for H(div) spaces based on curved meshes for two-dimensional regions or manifolds. Journal of Computational and Applied Mathematics, vol. 301, pp. 241”“258.

Devloo, P. R. B., Bravo, C. M. A., & Rylo, C. M. A., 2009. Systematic and generic construction of shape functions for p-adaptive meshes of multidimensional finite elements, Comput. Methods Appl. Mech. Engrg., vol. 198, pp. 1716”“1725.

Devloo, P. R. B., Farias, A. M., Gomes, S. M., & Siqueira, D., 2016. Two-dimensional hp”“adaptive finite element spaces for mixed formulations. Mathematics and Computers in Simulation (Print), vol. 126, pp. 104”“122.

N´ed´elec, J. C., 1980. Mixed finite elements in R3. Numer. Math., vol. 35, pp. 315-?341.

Lucci, P. C. A., 2009. Descric¸ ˜ao Matem´atica de Geometrias Curvas por Interpolac¸ ˜ao Transfinita, Master dissertation, Unicamp.

Raviart, P. A., & Thomas, J. M., 1977. A mixed finite element method for 2nd order elliptic problems. Lect. Note Math., vol. 606, pp. 292-?315.

Siqueira, D., Devloo, P. R. B., & Gomes, S. M., 2013. A new procedure for the construction of hierarchical high order Hdiv and Hcurl finite element spaces, Journal of Computational and Applied Mathematics, vol. 240, p. 204”“214.




Como Citar

R. B. Devloo, P., Durán, O., M. Gomes, S., & Shauer, N. (2017). HIGH ORDER FINITE ELEMENT BASES FOR H(div) SPACES BASED ON 3D ADAPTIVE CURVED MESHES. Revista Interdisciplinar De Pesquisa Em Engenharia, 2(34), 21–37. https://doi.org/10.26512/ripe.v2i34.21806