Hierarchical Divergence-Conforming Vector Bases for Pyramid Cells

Divergence-conforming hierarchical vector bases for the pyramid consist of face- and volume-based functions obtained by a simple procedure that uses new paradigm recently introduced this author to produce bases. In order define bases’ order, starts mapping pyramids into cube Cartesian space, which we call grandparent where basis their divergences take on polynomial form. Then get face-based zero first order. Functions arbitrarily high are multiplying lowest independent scalar polynomials higher Our conform those other differently shaped elements allow use hybrid meshes, while multiplicative construction technique generates right away functions. The completeness is demonstrated all obtain suitably normalized; expression involves orthogonal easy implement alleviate loss linear independence.