
The Hodge Laplacian on Axisymmetric Domains
We study the mixed formulation of the abstract Hodge Laplacian on axisym...
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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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On the analysis and approximation of some models of fluids over weighted spaces on convex polyhedra
We study the Stokes problem over convex, polyhedral domains on weighted ...
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Exact sequences on WorseyFarin Splits
We construct several smooth finite element spaces defined on three–dimen...
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Weak discrete maximum principle of finite element methods in convex polyhedra
We prove that the Galerkin finite element solution u_h of the Laplace eq...
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Nonlinear dimension reduction for surrogate modeling using gradient information
We introduce a method for the nonlinear dimension reduction of a highdi...
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Semantic 3D Reconstruction with Finite Element Bases
We propose a novel framework for the discretisation of multilabel probl...
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Multigrid in H(div) on Axisymmetric Domains
In this paper, we will construct and analyze a multigrid algorithm that can be applied to weighted H(div)problems on a twodimensional domain. These problems arise after performing a dimension reduction to a threedimensional axisymmetric H(div)problem. We will use recently developed Fourier finite element spaces that can be applied to axisymmetric H(div)problems with general data. We prove that if the axisymmetric domain is convex, then the multigrid Vcycle with modern smoothers will converge uniformly with respect to the meshsize.
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