Affiliation:
1. TU Chemnitz , Chemnitz , Germany
Abstract
Abstract
Recently,
H
(
div
)
\mathbf{H}(\mathrm{div})
-conforming finite element families were proven to be successful on anisotropic meshes, with the help of suitable interpolation error estimates.
In order to ensure corresponding large-scale computation, this contribution provides novel Raviart–Thomas basis functions, robust regarding the anisotropy of a given triangulation.
This new set of basis functions on simplices uses a hierarchical approach, and the orientation of the basis functions is inherited from the lowest-order case.
In the higher-order case, the new basis functions can be written as a combination of the lowest-order Raviart–Thomas elements and higher-order Lagrange-elements.
This ensures robustness regarding the mesh anisotropy and assembling strategies as demonstrated in the numerical experiments.
Subject
Applied Mathematics,Computational Mathematics,Numerical Analysis
Cited by
1 articles.
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1. Recent Advances in Finite Element Methods;Computational Methods in Applied Mathematics;2023-07-25