On adaptive anisotropic mesh optimization for convection-diffusion problems

Result code in 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>
Result on the web
<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>

Result language
angličtina
Original language name
On adaptive anisotropic mesh optimization for convection-diffusion problems
Original language description
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.
Czech name
—
Czech description
—

Type
J<sub>imp</sub> - Article in a specialist periodical, which is included in the Web of Science database
CEP classification
—
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
2025
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

Similar results(10)