Conservative and Accurate Solution Transfer Between High-Order and Low-Order Refined Finite Element Spaces

Kolev, Tzanio; Pazner, Will

doi:10.1137/21m1403916

Title: Conservative and Accurate Solution Transfer Between High-Order and Low-Order Refined Finite Element Spaces

Journal Article · 04 January 2022 · SIAM Journal on Scientific Computing

DOI: https://doi.org/10.1137/21m1403916 · OSTI ID:1959509

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Lawrence Livermore National Lab. (LLNL), Livermore, CA (United States)

Here, 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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Research Organization:: Lawrence Livermore National Laboratory (LLNL), Livermore, CA (United States)

Sponsoring Organization:: USDOE National Nuclear Security Administration (NNSA)

Grant/Contract Number:: AC52-07NA27344

OSTI ID:: 1959509

Report Number(s):: LLNL-JRNL-819814; 1030934

Journal Information:: SIAM Journal on Scientific Computing, Journal Name: SIAM Journal on Scientific Computing Journal Issue: 1 Vol. 44; ISSN 1064-8275

Publisher:: Society for Industrial and Applied Mathematics (SIAM)Copyright Statement

Country of Publication:: United States

Language:: English

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97 MATHEMATICS AND COMPUTING
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