Convergence of Anisotropic Mesh Adaptation via Metric Optimization
Name
20m1338721.pdf
Description
Published version
Size
1.05 MB
Format
Adobe PDF
Checksum (MD5)
5e35aefa113a32f67a654f8c55458af5
Author(s)
Carson, Hugh A
Allmaras, Steven
Galbraith, Marshall
Darmofal, David
Date Issued
June 2, 2022
Journal
SIAM Journal on Numerical Analysis
Publisher
Society for Industrial & Applied Mathematics (SIAM)
Citation
Carson, Hugh A, Allmaras, Steven, Galbraith, Marshall and Darmofal, David. 2022. "Convergence of Anisotropic Mesh Adaptation via Metric Optimization." SIAM Journal on Numerical Analysis, 60 (3).
Version
Final published version
Abstract
Adaptive finite element methods (AFEMs) are an increasingly common means of automatically controlling error in numerical simulations. Proofs of convergence and rate of convergence exist for AFEMs; however, these proofs typically rely upon a nested structure for the sequence of meshes. A metric adaptive finite element method (MAFEM) utilizes the continuous mesh model and instead seeks to optimize a Riemannian metric field for a given cost, from which a mesh is generated. This meshing process results in a sequence of nonnested meshes. In this paper we introduce a proof of convergence for a class of MAFEM, utilizing an optimization statement to relate the error on the sequence of meshes. In addition, we prove that such a sequence of meshes will demonstrate the optimal asymptotic rate of convergence for a given polynomial order. Finally some numerical results demonstrate the performance of the algorithm for a singularly perturbed linear advection diffusion problem.
MIT Department
Massachusetts Institute of Technology. Center for Computational Science and Engineering
Massachusetts Institute of Technology. Department of Aeronautics and Astronautics
Terms of Use
Article is made available in accordance with the publisher's policy and may be subject to US copyright law. Please refer to the publisher's site for terms of use.
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DOI of Published Version
https://doi.org/10.1137/20M1338721
