Minimal degree () and () conforming finite elements on polytopal meshes
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This article is published in Mathematics of Computation.The article was published on 2016-10-27 and is currently open access. It has received 28 citations till now. The article focuses on the topics: Mixed finite element method & Finite element exterior calculus.read more
Citations
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A Divergence Free Weak Virtual Element Method for the Stokes Problem on Polytopal Meshes
Long Chen,Long Chen,Feng Wang +2 more
TL;DR: Some virtual element methods on polytopal meshes for the Stokes problem are proposed and analyzed, and the main feature is that it exactly preserves the divergence free constraint, and therefore the error estimates for the velocity does not explicitly depend on the pressure.
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High-order polygonal discontinuous Petrov–Galerkin (PolyDPG) methods using ultraweak formulations
TL;DR: In this paper, the authors presented the first endeavor in using ultraweak formulations to implement high-order polygonal finite element methods via the discontinuous Petrov-Galerkin (DPG) methodology.
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Construction of scalar and vector finite element families on polygonal and polyhedral meshes.
TL;DR: The construction recovers well-known bases for the lowest order Nédélec, Raviart–Thomas, and Brezzi–Douglas–Marini elements on simplicial meshes and generalizes the notion of Whitney forms to non-simplicial convex polygons and polyhedra.
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Fully discrete polynomial de Rham sequences of arbitrary degree on polygons and polyhedra
TL;DR: In this paper, a fully discrete polynomial de Rham sequence of arbitrary degree on polygons and polyhedra is constructed, and the spaces and operators that appear in these sequences are directly amenable to computer implementation.
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Operator-adapted wavelets for finite-element differential forms
TL;DR: An operator-adapted multiresolution analysis for finite-element differential forms from a given continuous, linear, bijective, and self-adjoint positive-definite operator L is introduced, which can derive both scalar-valued and vector-valued wavelets block-diagonalizing a prescribed operator.
References
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Mixed finite elements in ℝ 3
TL;DR: In this article, the authors present two families of non-conforming finite elements, built on tetrahedrons or on cubes, which are respectively conforming in the spacesH(curl) and H(div).
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Centroidal Voronoi Tessellations: Applications and Algorithms
TL;DR: Some applications of centroidal Voronoi tessellations to problems in image compression, quadrature, finite difference methods, distribution of resources, cellular biology, statistics, and the territorial behavior of animals are given.
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Approximation by finite element functions using local regularization
TL;DR: In this paper, the authors give an elementary proof of a theorem of approximation of Sobolev spaces by fimte éléments without to use classical interpolation, which allows us in some cases to fit boundary conditions.