Conforming polygonal finite elements

By Natarajan Sukumar, A. Tabarraei. 2004

488 citations recorded by the source corpus.

Subfields: Computational Mechanics, Mechanics of Materials

View Paper: https://www.semanticscholar.org/paper/6294bc9f246725fa6a5ec70ac05352eb7c8e57c4

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Computational Mechanics

1. L. Beirão da Veiga
2. Gianmarco Manzini
3. Stéphane P.A. Bordas
4. Natarajan Sukumar
5. Alessandro Russo
6. Giuseppe Vacca
7. E. Ooi
8. Hung Nguyen-Xuan

In Mechanics of Materials

1. Stéphane P.A. Bordas
2. Gianmarco Manzini
3. L. Beirão da Veiga
4. E. Ooi
5. Natarajan Sukumar
6. Sundararajan Natarajan
7. Hung Nguyen-Xuan
8. Alessandro Russo

Citations in the corpus

• New perspectives on polygonal and polyhedral finite element methods (2014, methodology): “Along with the advances of barycentric coordinates in graphics, there has been a parallel development of barycentric finite element and boundary element methods on polygons and polyhedra [5, 39, 40, 41, 17, 42, 43, 44, 45, 46, 47, 48, 49, 50], with recent applications in fracture modeling [51, 52, 5”
• Scaled boundary polygons with application to fracture analysis of functionally graded materials (2014, methodology): “A polygon mesh can be generated from Delaunay triangulation [7] or Voronoi diagrams [1].”
• A Plane Wave Virtual Element Method for the Helmholtz Problem (2015, background): “, [47]), that can be considered also as VEM space of lowest order; see [36] for other choices of generalized barycentric coordinates.”
• A multigrid algorithm for the $p$-version of the Virtual Element Method (2017, methodology): “Examples of methods that have been proposed so far include mimetic finite differences [20, 35, 51, 52], polygonal finite element methods [58, 59], discontinuous-Galerkin finite element methods [4, 5, 9, 16, 37, 38, 40] hybridizable and hybrid high hrder methods [42, 43, 45], BEM-based FEM [56] and g”
• Convergence analysis of virtual element methods for semilinear parabolic problems on polygonal meshes (2018, methodology): “[15]), in the VEM, one does not require explicit computation of shape functions corresponding to the finite dimensional spaces.”
• Crack propagation modelling in functionally graded materials using scaled boundary polygons (2015, methodology): “These include, for example, the use of the Wachpress shape functions (Wachspress 1975), natural neighbour interpolants (Sukumar and Tabarraei 2004), and the Voronoi cell FEM (Ghosh and Moorthy 1995).”
• Honeycomb Wachspress finite elements for structural topology optimization (2009, methodology): “Wachspress rational shape functions satisfy the necessary conditions for conforming Galerkin approximations (Sukumar and Tabarraei 2004; Sukumar and Malsch 2005).”
• Basic principles of Virtual Element Methods (2013, methodology): “This of course makes the method now closer to other attempts to generalize Finite Elements on polygons, like the PFEM (Polygonal Finite Element Methods, see for instance [29, 30]) or the Extended Finite Element Methods (see [22] and the references therein).”
• Review of Discontinuous Galerkin Finite Element Methods for Partial Differential Equations on Complicated Domains (2016, methodology): “In the conforming setting, we mention the CFE method [33, 32], the Polygonal Finite Element Method [45], and the Extended Finite Element Method [27].”