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Licensed Unlicensed Requires Authentication Published online by De Gruyter March 26, 2024

A Numerical Study of a Stabilized Hyperbolic Equation Inspired by Models for Bio-Polymerization

  • Lisa Davis , Monika Neda , Faranak Pahlevani , Jorge Reyes ORCID logo EMAIL logo and Jiajia Waters

Abstract

This report investigates a stabilization method for first order hyperbolic differential equations applied to DNA transcription modeling. It is known that the usual unstabilized finite element method contains spurious oscillations for nonsmooth solutions. To stabilize the finite element method the authors consider adding to the first order hyperbolic differential system a stabilization term in space and time filtering. Numerical analysis of the stabilized finite element algorithms and computations describing a few biological settings are studied herein.

Award Identifier / Grant number: DMS-1951510

Award Identifier / Grant number: DMS-1951563

Funding statement: The contribution of the authors Dr. Davis and Dr. Pahlevani was supported by the National Science Foundation under Awards DMS-1951510 and DMS-1951563.

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Received: 2023-10-10
Revised: 2024-02-23
Accepted: 2024-03-12
Published Online: 2024-03-26

© 2024 Walter de Gruyter GmbH, Berlin/Boston

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