• Corpus ID: 12187469

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

  title={Low-order continuous finite element spaces on hybrid non-conforming hexahedral-tetrahedral meshes},
  author={Maxence Reberol and Bruno L{\'e}vy},
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… 

Figures from this paper

Robust hex-dominant mesh generation using field-guided polyhedral agglomeration
A robust and efficient field-aligned volumetric meshing algorithm that produces hex-dominant meshes, i.e. meshes that are predominantly composed of hexahedral elements while containing a small number of irregular polyhedra, which allows this method to generate meshes with an exceptionally high amount of isotropy.
Enabling four-dimensional conformal hybrid meshing with cubic pyramids
A novel refinement strategy for four-dimensional hybrid meshes based on cubic pyramids and a new class of fully symmetric quadrature rules with positive weights are generated for the cubic pyramid.
Feature Preserving Octree‐Based Hexahedral Meshing
An octree‐based algorithm to tessellate the interior of a closed surface with hexahedral cells that explicitly preserves sharp features of the original input and has a maximal, user‐controlled distance deviation from the input surface.
Maillages hex-dominants : génération, simulation et évaluation
Cette these s'interesse a la generation, a l'utilisation et a l'evaluation des maillages hex-dominants, composes d'hexaedres et de tetraedres, dans la cadre de la simulation numerique par la methode


High-order discontinuous Galerkin method for time-domain electromagnetics on non-conforming hybrid meshes
  • H. Fahs
  • Computer Science
    Math. Comput. Simul.
  • 2015
Indirect unstructured hex-dominant mesh generation using tetrahedra recombination
Corner-point gridding is widely used in reservoir and basin modeling but generally yields approximations in the representation of geological interfaces. This paper introduces an indirect method to
Practical hex-mesh optimization via edge-cone rectification
This work recast hex quality improvement as an optimization of the shape of overlapping cones, or unions, of tetrahedra surrounding every directed edge in the hex mesh, and forms a novel framework for optimizing hex-mesh quality capable of generating inversion-free high-quality meshes from such poor initial inputs.
A method is proposed whereby an existing non-conforming, mixed hexahedra-tetrahedra element mesh, is altered to conform by the insertion and formation of five-node or thirteen-node pyramids. Local
A frontal approach to hex-dominant mesh generation
It is shown that the percentage of recombined hexahedra strongly depends on the location of the vertices in the initial 3D mesh, and that the execution times are reasonable and non-conformal quadrilateral faces adjacent to triangular faces are present in the final meshes.
Higher-order Finite Elements for Hybrid Meshes Using New Nodal Pyramidal Elements
Numerical results demonstrate the efficiency of hybrid meshes compared to pure tetrahedral meshes or hexahedral meshes obtained by splitting tetrahedra into hexahedra.
Higher‐order discontinuous Galerkin method for pyramidal elements using orthogonal bases
A new family of high‐order pyramidal finite elements using orthogonal basis functions which can be used in hybrid meshes including hexahedra, tetrahedra , wedges, and pyramids are proposed.
Construction of tetrahedral meshes of degree two
There is a need for finite elements of degree two or more to solve various PDE problems and a method to construct such meshes in the case of tetrahedral element of level two is discussed.
Spectral / hp Methods For Elliptic Problems on Hybrid Grids
First, high-order hierarchical expansions with exponential convergence for smooth solutions are developed, which are substantially less sensitive to grid distortions and employ hybrid grids consisting of tetrahedra, hexaheda, prisms, and pyramids that facilitate great discretisation flexibility and lead to substantial memory savings.
Conforming arbitrary order hexahedral/tetrahedral hybrid discretisation
A new method for constructing H ( curl ) or H ( div ) conforming hexahedral/tetrahedral hybrid meshes of arbitrary discretisation order is presented, avoiding the need for pyramidal or other joining element types.