Work

Convergence in the incompressible limit of the corner singularities

Year: 2025

Type: article

Abstract: In this paper, we treat the corner singularity expansion and its convergence result regarding the penalized system obtained by eliminating the pressure variable in the Stokes problem of incompressible flow. The penalized problem is a kind of the Lamé system, so we first discuss the corner singularity theory of the Lamé system with inhomogeneous Dirichlet boundary condition on a non-convex polygon. Considering the inhomogeneous condition, we show the decomposition of its solution, composed of singular parts and a smoother remainder near a re-entrant corner, and furthermore, we provide the explicit formulae of coefficients in singular parts. In particular, these formulae can be used in the development of highly accurate numerical scheme. In addition, we formulate coefficients in singular parts regarding the Stokes equations with inhomogeneous boundary condition and non-divergence-free property of velocity field, and thus we show the convergence results of coefficients in singular parts and remainder regarding the concerned penalized problem.

Source: Journal of Differential Equations

DOI: 10.1016/j.jde.2025.113415

Authors: Hyung Jun Choi, Seonghak Kim, Youngwoo Koh

Institutions: Korea University of Technology and Education, Kyungpook National University, Kongju National University

Language: English

Topic: Advanced Numerical Methods in Computational Mathematics

Subfield: Computational Mechanics

Field: Engineering

Domain: Physical Sciences

Open Access status: hybrid

Estimated APC paid: $3,550