Influence of weighted function exponent in WFEM on error of solution for hydrodynamic problems with singularity

A. V. Rukavishnikov

Dalʹnevostočnyj matematičeskij žurnal, Tome 22 (2022) no. 2, pp. 225-231.

Résumé

The concept of an $R_{\nu}$-generalized solution for a hydrodynamic problem with reentrant corner on the boundary of a polygonal domain is defined. An approximate method for solving the problem is constructed. A numerical analysis is carried out and the question of the influence of the weighted function exponent in the weighted finite element method on the error of the solution in the vicinity of the reentrant corner in the norm of the space $C(\bar{\Omega})$ is experimentally studied. A comparative analysis has been carried out and the advantage of the weighted method over the classical approach has been shown.

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