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Advanced Numerical Methods in the Mathematical Sciences

Federico Fuentes, University of Texas at Austin
Pyramid High Order Exact Sequence Shape Functions


In 'hybrid meshes', where both tetrahedra and hexahedra are present, pyramids and prisms are fundamental since they act as connecting elements in the mesh. Due to the mathematical requirement of having to use rational polynomials as opposed to the regular polynomials used in the other elements, commuting exact sequence high order finite element spaces are very hard to construct for the pyramid. Recently such a set of spaces was proposed in [1]. Here a set of compatible hierarchical shape functions spanning those spaces are presented for each of the four energy spaces in coordinate free format satisfying many desirable properties. The work is complemented by other sets of shape functions for the other three elements (tetrahedra, hexahedra and prisms) which are presented in [2] and implemented in a freely available library online at [3].


  1. N. Nigam and J. Phillips, High-Order Conforming Finite Elements on Pyramids, IMA Journal of Numerical Analysis () 32(2):448-483.
  2. F. Fuentes, B. Keith, L. Demkowicz, and S. Nagaraj, High Order Orientation Embedded Finite Element Shape Functions for the Exact Sequence Elements of all Shapes, ICES Report 15-07, UT Austin ().
  3. The ESEAS library: