A multiscale hybrid method

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Barrenechea, Gabriel R. and Gomes, Antonio Tadeu A. and Paredes, Diego (2024) A multiscale hybrid method. SIAM Journal on Scientific Computing, 46 (3). A1628 - A1657. ISSN 1064-8275 (https://doi.org/10.1137/22M1542556)

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Abstract

In this work we propose, analyze, and test a new multiscale finite element method called Multiscale Hybrid (MH) method. The method is built as a close relative to the Multiscale Hybrid Mixed (MHM) method, but with the fundamental difference that a novel definition of the Lagrange multiplier is introduced. The practical implication of this is that both the local problems to compute the basis functions, as well as the global problem, are elliptic, as opposed to the MHM method (and also other previous methods) where a mixed global problem is solved, and constrained local problems are solved to compute the local basis functions. The error analysis of the method is based on a hybrid formulation, and a static condensation process is done at the discrete level, so the final global system only involves the Lagrange multipliers. We tested the performance of the method by means of numerical experiments for problems with multiscale coefficients, and we carried out comparisons with the MHM method in terms of performance, accuracy, and memory requirements.

ORCID iDs

Barrenechea, Gabriel R. ORCID logoORCID: https://orcid.org/0000-0003-4490-678X, Gomes, Antonio Tadeu A. and Paredes, Diego;
  • Item type:Article
    ID code:88570
    Dates:
    Date
    Event
    June 2024
    Published
    13 May 2024
    Published Online
    25 January 2024
    Accepted
    21 December 2022
    Submitted
    Subjects:Science > Mathematics
    Department:Faculty of Science > Mathematics and Statistics
    Depositing user: Pure Administrator
    Date deposited:26 Mar 2024 12:48
    Last modified:21 Dec 2024 01:28
    URI:https://strathprints.strath.ac.uk/id/eprint/88570
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