HIGH ORDER FINITE ELEMENT BASES FOR H(div) SPACES BASED ON 3D ADAPTIVE CURVED MESHES - R. B. Devloo, Philippe; Durán, Omar; M. Gomes, Sônia; Shauer, Nathan (Revista Interdisciplinar de Pesquisa em Engenharia, 2017)
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.