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dc.contributor.authorCao, Weiming
dc.contributor.authorCarretero-Gonzalez, Ricardo
dc.contributor.authorHuang, Weizhang
dc.contributor.authorRussell, Robert D.
dc.identifier.citationCao, Weiming., Carretero-GOnzalez, Ricardo., Huang, Weizhang., Russell, Robert D. "Variational mesh adaptation methods for axisymmetrical problems." SIAM J. Numer. Anal., 41(1), 235–257. (23 pages).
dc.descriptionThis is the published version, also available here:
dc.description.abstractWe 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 $\lambda_1$ and $\lambda_2$ satisfying $\lambda_1(0) < \lambda_2(0)$ will make the mesh denser at $r=0$ than in the surrounding area whether or not $\lambda_1$ has a maximum value at r=0. The purpose can also be served by choosing $\lambda_1$ to have a local maximum at r=0 when a Winslow-type monitor function with $\lambda_1(r) = \lambda_2(r)$ is employed. On the other hand, it is shown that the traditional functional provides little control over mesh concentration around a ring $r = r_\lambda > 0$ by choosing $\lambda_1$ and $\lambda_2$.

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.
dc.publisherSociety for Industrial and Applied Mathematicsen_US
dc.titleVariational Mesh Adaptation Methods for Axisymmetrical Problemsen_US
kusw.kuauthorHuang, Weizhang
kusw.oanotesOn author or institutional website or online repository. Non-commercial. Publisher copyright must be acknowledged. Publisher's version/PDF may be used.en_US
kusw.oaversionScholarly/refereed, publisher version
kusw.oapolicyThis item does not meet KU Open Access policy criteria.

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