'Society for Industrial & Applied Mathematics (SIAM)'
Doi
Abstract
This is the published version, also available here: http://dx.doi.org/10.1137/S0036142902401591.We study variational mesh adaptation for axially symmetric solutions to two-dimensional problems. The study is focused on the relationship between the mesh density distribution and the monitor function and is carried out for a traditional functional that includes several widely used variational methods as special cases and a recently proposed functional that allows for a weighting between mesh isotropy (or regularity) and global equidistribution of the monitor function. The main results are stated in Theorems \ref{thm4.1} and \ref{thm4.2}. For axially symmetric problems, it is natural to choose axially symmetric mesh adaptation. To this end, it is reasonable to use the monitor function in the form G = \lambda_1(r) {\mbox{\boldmath {e}}}_r {\mbox{\boldmath {e}}}_r^T + \lambda_2(r) {\mbox{\boldmath {e}}} _\theta {\mbox{\boldmath {e}}}_\theta^T , where {\mbox{\boldmath {e}}}_r and {\mbox{\boldmath {e}}}_\theta are the radial and angular unit vectors.
It is shown that when higher mesh concentration at the origin is desired, a choice of Ī»1ā and Ī»2ā satisfying Ī»1ā(0)0 by choosing Ī»1ā and Ī»2ā.
In contrast, numerical results show that the new functional provides better control of the mesh concentration through the monitor function. Two-dimensional numerical results are presented to support the analysis