Well-balanced convex limiting for finite element discretizations of steady convection-diffusion-reaction equations

Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F00216208%3A11320%2F24%3A10489231" target="_blank" >RIV/00216208:11320/24:10489231 - isvavai.cz</a>
Result on the web
<a href="https://verso.is.cuni.cz/pub/verso.fpl?fname=obd_publikace_handle&handle=L.euDrYqTl" target="_blank" >https://verso.is.cuni.cz/pub/verso.fpl?fname=obd_publikace_handle&handle=L.euDrYqTl</a>
DOI - Digital Object Identifier
<a href="http://dx.doi.org/10.1016/j.jcp.2024.113305" target="_blank" >10.1016/j.jcp.2024.113305</a>

Result language
angličtina
Original language name
Well-balanced convex limiting for finite element discretizations of steady convection-diffusion-reaction equations
Original language description
We address the numerical treatment of source terms in algebraic flux correction schemes for steady convection-diffusion-reaction (CDR) equations. The proposed algorithm constrains a continuous piecewise-linear finite element approximation using a monolithic convex limiting (MCL) strategy. Failure to discretize the convective derivatives and source terms in a compatible manner produces spurious ripples, e.g., in regions where the coefficients of the continuous problem are constant and the exact solution is linear. We cure this deficiency by incorporating source term components into the fluxes and intermediate states of the MCL procedure. The design of our new limiter is motivated by the desire to preserve simple steady-state equilibria exactly, as in well-balanced schemes for the shallow water equations. The results of our numerical experiments for two-dimensional CDR problems illustrate potential benefits of well-balanced flux limiting in the scalar case.
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
10102 - Applied mathematics

Project
<a href="/en/project/GA22-01591S" target="_blank" >GA22-01591S: Mathematical theory and numerical analysis for equations of viscous newtonian compressible fluids</a><br>
Continuities
P - Projekt vyzkumu a vyvoje financovany z verejnych zdroju (s odkazem do CEP)

Publication year
2024
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

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