Conservative and Accurate Solution Transfer Between High-Order and Low-Order Refined Finite Element Spaces
Abstract
In this paper we introduce general transfer operators between high-order and low-order refined finite element spaces that can be used to couple high-order and low-order simulations. Under natural restrictions on the low-order refined space we prove that both the high-to-low-order and low-to-high-order linear mappings are conservative, constant preserving, and high-order accurate. While the proof holds for affine geometries, numerical experiments indicate that the results hold for more general curved meshes. We present several numerical results confirming our analysis and demonstrate the utility of the new mappings in the context of adaptive mesh refinement and conservative multidiscretization coupling.
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© 2022, Society for Industrial and Applied Mathematics.
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Submitted: 9 March 2021
Accepted: 1 September 2021
Published online: 5 January 2022
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Lawrence Livermore National Laboratory https://doi.org/10.13039/100006227 : DE-AC52-07NA27344
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