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74,133
Merging the Bramble . . . ONTO FINITE ELEMENT SPACES
, 2001
"... Suppose S⊂H1 (Ω) is a finitedimensional linear space based on a triangulation T of a domain Ω, and let Π: L2 (Ω) → L2 (Ω) denote the L2projection onto S. Provided the mass matrix of each element T ∈T and the surrounding meshsizes obey the inequalities due to Bramble, Pasciak, and Steinbach or ..."
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Suppose S⊂H1 (Ω) is a finitedimensional linear space based on a triangulation T of a domain Ω, and let Π: L2 (Ω) → L2 (Ω) denote the L2projection onto S. Provided the mass matrix of each element T ∈T and the surrounding meshsizes obey the inequalities due to Bramble, Pasciak, and Steinbach
De Rham Diagram for hp Finite Element Spaces
, 1999
"... We prove that the hp finite elements for H(curl) spaces, introduced in [2], fit into a general de Rham diagram involving hp approximations. The corresponding interpolation operators generalize the notion of hp interpolation introduced in [7] and are different from the classical operators of Nedelec ..."
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Cited by 27 (7 self)
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We prove that the hp finite elements for H(curl) spaces, introduced in [2], fit into a general de Rham diagram involving hp approximations. The corresponding interpolation operators generalize the notion of hp interpolation introduced in [7] and are different from the classical operators of Nedelec
A Unified Topological Layer for Finite Element Space
"... Abstract. A unified topological layer for mesh generation has been created to benefit from current development, to reuse existing, well tested and reliable methods, such as the Delaunay or the Advancing Front mesh generation approach, and to combine them to be able to interchange these methods, with ..."
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Abstract. A unified topological layer for mesh generation has been created to benefit from current development, to reuse existing, well tested and reliable methods, such as the Delaunay or the Advancing Front mesh generation approach, and to combine them to be able to interchange these methods, without taking a detour using file formats. In addition, by modularizing existing meshing kernels, this approach allows to not only have one meshing interface for arbitrary dimensions, but also to have the possibility at hand to independently combine different meshing strategies.
Inversetype estimates on hpfinite element spaces and applications
 Math. Comp
, 2008
"... Abstract. This work is concerned with the development of inversetype inequalities for piecewise polynomial functions and, in particular, functions belonging to hpfinite element spaces. The cases of positive and negative Sobolev norms are considered for both continuous and discontinuous finite el ..."
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Cited by 10 (0 self)
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Abstract. This work is concerned with the development of inversetype inequalities for piecewise polynomial functions and, in particular, functions belonging to hpfinite element spaces. The cases of positive and negative Sobolev norms are considered for both continuous and discontinuous finite
A General Transfer Operator for Arbitrary Finite Element Spaces
, 2000
"... We construct and analyze a transfer operator from any given (e.g. nonconforming) to an arbitrary desired (e.g. higher order conforming) finite element space. This transfer operator also defines a stable interpolation operator for elementwise smooth functions satisfying Dirichlet boundary conditions ..."
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Cited by 4 (1 self)
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We construct and analyze a transfer operator from any given (e.g. nonconforming) to an arbitrary desired (e.g. higher order conforming) finite element space. This transfer operator also defines a stable interpolation operator for elementwise smooth functions satisfying Dirichlet boundary
9 SpringerVerlag 1986 On the MultiLevel Splitting of Finite Element Spaces
"... Summary. In this paper we analyze the condition number of the stiffness matrices arising in the discretization of selfadjoint and positive definite plane elliptic boundary value problems of second order by finite element methods when using hierarchical bases of the finite element spaces instead of t ..."
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Summary. In this paper we analyze the condition number of the stiffness matrices arising in the discretization of selfadjoint and positive definite plane elliptic boundary value problems of second order by finite element methods when using hierarchical bases of the finite element spaces instead
On Some Applications of the ...Stable WaveletLike Hierarchical Finite Element Space Decompositions
 In: The Methematics of Finite Elements and Applications, Highlights
, 1996
"... . In this paper we first review the construction of stable Riesz bases for finite element spaces with respect to Sobolev norms. Then, we construct optimal order multilevel preconditioners for the matrices in the normal form of the equations arising in the finite element discretization of nonsymmet ..."
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Cited by 1 (0 self)
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. In this paper we first review the construction of stable Riesz bases for finite element spaces with respect to Sobolev norms. Then, we construct optimal order multilevel preconditioners for the matrices in the normal form of the equations arising in the finite element discretization of non
Interpolation estimate for a finiteelement space with embedded discontinuities
, 2012
"... We consider a recently proposed finiteelement space that consists of piecewise affine functions with discontinuities across a smooth given interface Γ (a curve in two dimensions, a surface in three dimensions). Contrary to existing extended finite element methodologies, the space is a variant of t ..."
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We consider a recently proposed finiteelement space that consists of piecewise affine functions with discontinuities across a smooth given interface Γ (a curve in two dimensions, a surface in three dimensions). Contrary to existing extended finite element methodologies, the space is a variant
Multigrid Techniques for Simple Discretely DivergenceFree Finite Element Spaces
"... . We derive some basic properties for a class of discretely divergence free finite elements. These make possible a new proof of the smoothing property in a standard multigrid algorithm for the Stokes equations. In addition with appropriate divergencefree grid transfer routines of second order accu ..."
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accuracy we get the full multigrid convergence. We demonstrate how to develop and implement efficiently these operators and confirm our theoretical results by numerical tests. 1. The simple nonconforming finite element spaces We consider the usual weak formulation of the steady Stokes problem
Results 1  10
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74,133