Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
4638234 | Journal of Computational and Applied Mathematics | 2016 | 21 Pages |
Abstract
It is shown in Choi and Kweon (2013) that a solution of the Navier–Stokes equations with no-slip boundary condition on a non-convex polygon can be written as [u,p]=C1[Φ1,ϕ1]+C2[Φ2,ϕ2]+[ur,pr] near each non-convex vertex, where [ur,pr]∈H2×H1, [Φi,ϕi][Φi,ϕi] are corner singularity functions for the Stokes problem with no-slip condition, and Ci∈RCi∈R are coefficients which are called the stress intensity factors. We design a finite element method to approximate the coefficients CiCi and the regular part [ur,pr], show the unique existence of the approximations, and derive their error estimates. Some numerical examples are given, confirming convergence rates for the approximations.
Related Topics
Physical Sciences and Engineering
Mathematics
Applied Mathematics
Authors
Hyung Jun Choi, Jae Ryong Kweon,