
H1conforming finite element cochain complexes and commuting quasiinterpolation operators on cartesian meshes
A finite element cochain complex on Cartesian meshes of any dimension ba...
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A Construction of C^r Conforming Finite Element Spaces in Any Dimension
This paper proposes a construction of local C^r interpolation spaces and...
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There are 174 Triangulations of the Hexahedron
This article answers an important theoretical question: How many differe...
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Connections Between Finite Difference and Finite Element Approximations
We present useful connections between the finite difference and the fini...
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GibbsRinging Artifact Removal Based on Local Subvoxelshifts
Gibbsringing is a well known artifact which manifests itself as spuriou...
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UFL Dual Spaces, a proposal
This white paper highlights current limitations in the algebraic closure...
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Evaluating the Quality of Finite Element Meshes with Machine Learning
This paper addresses the problem of evaluating the quality of finite ele...
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Gibbs Phenomena for L^qBest Approximation in Finite Element Spaces  Some Examples
Recent developments in the context of minimum residual finite element methods are paving the way for designing finite element methods in nonstandard function spaces. This, in particular, permits the selection of a solution space in which the best approximation of the solution has desirable properties. One of the biggest challenges in designing finite element methods are nonphysical oscillations near thin layers and jump discontinuities. In this article we investigate Gibbs phenomena in the context of L^qbest approximation of discontinuities in finite element spaces with 1≤ q<∞. Using carefully selected examples, we show that on certain meshes the Gibbs phenomenon can be eliminated in the limit as q tends to 1. The aim here is to show the potential of L^1 as a solution space in connection with suitably designed meshes.
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