On adaptive anisotropic mesh optimization for convection-diffusion problems

Kód výsledku v IS VaVaI

<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F00216208%3A11320%2F25%3A10509012" target="_blank" >RIV/00216208:11320/25:10509012 - isvavai.cz</a>

Výsledek na webu

<a href="https://verso.is.cuni.cz/pub/verso.fpl?fname=obd_publikace_handle&handle=EYIPcmCYk8" target="_blank" >https://verso.is.cuni.cz/pub/verso.fpl?fname=obd_publikace_handle&handle=EYIPcmCYk8</a>

DOI - Digital Object Identifier

<a href="http://dx.doi.org/10.1016/j.cam.2025.116661" target="_blank" >10.1016/j.cam.2025.116661</a>

Jazyk výsledku

angličtina

Název v původním jazyce

On adaptive anisotropic mesh optimization for convection-diffusion problems

Popis výsledku v původním jazyce

Numerical solution of convection-dominated problems requires the use of layer-adapted anisotropic meshes. Since a priori construction of such meshes is difficult for complex problems, it is proposed to generate them in an adaptive way by moving the node positions in the mesh such that an a posteriori error estimator of the overall error of the approximate solution is reduced. This approach is formulated for a SUPG finite element discretization of a stationary convection-diffusion problem defined in a two-dimensional polygonal domain. The optimization procedure is based on the discrete adjoint technique and a SQP method using the BFGS update. The optimization of node positions is applied to a coarse grid only and the resulting anisotropic mesh is then refined by standard adaptive red-green refinement. Four error estimators based on the solution of local Dirichlet problems are tested and it is demonstrated that an L2 norm based error estimator is the most robust one. The efficiency of the proposed approach is demonstrated on several model problems whose solutions contain typical boundary and interior layers.

Název v anglickém jazyce

On adaptive anisotropic mesh optimization for convection-diffusion problems

Popis výsledku anglicky

Numerical solution of convection-dominated problems requires the use of layer-adapted anisotropic meshes. Since a priori construction of such meshes is difficult for complex problems, it is proposed to generate them in an adaptive way by moving the node positions in the mesh such that an a posteriori error estimator of the overall error of the approximate solution is reduced. This approach is formulated for a SUPG finite element discretization of a stationary convection-diffusion problem defined in a two-dimensional polygonal domain. The optimization procedure is based on the discrete adjoint technique and a SQP method using the BFGS update. The optimization of node positions is applied to a coarse grid only and the resulting anisotropic mesh is then refined by standard adaptive red-green refinement. Four error estimators based on the solution of local Dirichlet problems are tested and it is demonstrated that an L2 norm based error estimator is the most robust one. The efficiency of the proposed approach is demonstrated on several model problems whose solutions contain typical boundary and interior layers.

Druh

J_imp - Článek v periodiku v databázi Web of Science

CEP obor

—

OECD FORD obor

10102 - Applied mathematics

Projekt

<a href="/cs/project/GA22-01591S" target="_blank" >GA22-01591S: Matematická teorie a numerická analýza rovnic vazkých newtonovských stlačitelných tekutin</a><br>

Návaznosti

P - Projekt vyzkumu a vyvoje financovany z verejnych zdroju (s odkazem do CEP)

Rok uplatnění

2025

Kód důvěrnosti údajů

S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

Název periodika

Journal of Computational and Applied Mathematics

ISSN

0377-0427

e-ISSN

1879-1778

Svazek periodika

469

Číslo periodika v rámci svazku

1 December 2025

Stát vydavatele periodika

NL - Nizozemsko

Počet stran výsledku

17

Strana od-do

116661

Kód UT WoS článku

001464835000001

EID výsledku v databázi Scopus

2-s2.0-105001868312