Asymptotic-preserving hybridizable discontinuous Galerkin method for the Westervelt quasilinear wave equation

Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F67985840%3A_____%2F25%3A00617515" target="_blank" >RIV/67985840:_____/25:00617515 - isvavai.cz</a>
Result on the web
<a href="https://doi.org/10.1051/m2an/2024085" target="_blank" >https://doi.org/10.1051/m2an/2024085</a>
DOI - Digital Object Identifier
<a href="http://dx.doi.org/10.1051/m2an/2024085" target="_blank" >10.1051/m2an/2024085</a>

Result language
angličtina
Original language name
Asymptotic-preserving hybridizable discontinuous Galerkin method for the Westervelt quasilinear wave equation
Original language description
We discuss the asymptotic-preserving properties of a hybridizable discontinuous Galerkin method for the Westervelt model of ultrasound waves. More precisely, we show that the proposed method is robust with respect to small values of the sound diffusivity damping parameter δ by deriving low- and high-order energy stability estimates, and a priori error bounds that are independent of δ. Such bounds are then used to show that, when δ 0+, the method remains stable and the discrete acoustic velocity potential ψh(δ) converges to ψh(0), where the latter is the singular vanishing dissipation limit. Moreover, we prove optimal convergence rates for the approximation of the acoustic particle velocity variable u =∇ ψ. The established theoretical results are illustrated with some numerical experiments.
Czech name
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Czech description
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Type
J<sub>imp</sub> - Article in a specialist periodical, which is included in the Web of Science database
CEP classification
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OECD FORD branch
10101 - Pure mathematics

Project
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Continuities
I - Institucionalni podpora na dlouhodoby koncepcni rozvoj vyzkumne organizace

Publication year
2025
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

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