Skip to Main content Skip to Navigation

Low-order continuous finite element spaces on hybrid non-conforming hexahedral-tetrahedral meshes

Maxence Reberol 1 Bruno Lévy 1
1 ALICE - Geometry and Lighting
Inria Nancy - Grand Est, LORIA - ALGO - Department of Algorithms, Computation, Image and Geometry
Abstract : This article deals with solving partial differential equations with the finite element method on hybrid non-conforming hexahedral-tetrahedral meshes. By non-conforming, we mean that a quadrangular face of a hexahedron can be connected to two triangular faces of tetrahedra. We introduce a set of low-order continuous (C0) finite element spaces defined on these meshes. They are built from standard tri-linear and quadratic Lagrange finite elements with an extra set of constraints at non-conforming hexahedra-tetrahedra junctions to recover continuity. We consider both the continuity of the geometry and the continuity of the function basis as follows: the continuity of the geometry is achieved by using quadratic mappings for tetrahedra connected to tri-affine hexahedra and the continuity of interpolating functions is enforced in a similar manner by using quadratic Lagrange basis on tetrahedra with constraints at non-conforming junctions to match tri-linear hexahedra. The so-defined function spaces are validated numerically on simple Poisson and linear elasticity problems for which an analytical solution is known. We observe that using a hybrid mesh with the proposed function spaces results in an accuracy significantly better than when using linear tetrahedra and slightly worse than when solely using tri-linear hexahedra. As a consequence, the proposed function spaces may be a promising alternative for complex geometries that are out of reach of existing full hexahedral meshing methods.
Complete list of metadatas
Contributor : Maxence Reberol <>
Submitted on : Monday, May 9, 2016 - 5:22:52 PM
Last modification on : Friday, February 26, 2021 - 8:26:03 AM
Long-term archiving on: : Tuesday, November 15, 2016 - 11:43:02 PM


Files produced by the author(s)


  • HAL Id : hal-01313285, version 1
  • ARXIV : 1605.02626


Maxence Reberol, Bruno Lévy. Low-order continuous finite element spaces on hybrid non-conforming hexahedral-tetrahedral meshes. [Research Report] INRIA Nancy, équipe ALICE. 2016. ⟨hal-01313285⟩



Record views


Files downloads