dc.contributor.author Cao, Weiming dc.contributor.author Carretero-Gonzalez, Ricardo dc.contributor.author Huang, Weizhang dc.contributor.author Russell, Robert D. dc.date.accessioned 2015-02-25T21:49:49Z dc.date.available 2015-02-25T21:49:49Z dc.date.issued 2003-01-01 dc.identifier.citation Cao, 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). http://dx.doi.org/10.1137/S0036142902401591. en_US dc.identifier.uri http://hdl.handle.net/1808/16875 dc.description This is the published version, also available here: http://dx.doi.org/10.1137/S0036142902401591. en_US dc.description.abstract 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 $\lambda_1$ 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. en_US dc.publisher Society for Industrial and Applied Mathematics en_US dc.title Variational Mesh Adaptation Methods for Axisymmetrical Problems en_US dc.type Article kusw.kuauthor Huang, Weizhang kusw.kudepartment Mathematics en_US dc.identifier.doi 10.1137/S0036142902401591 kusw.oaversion Scholarly/refereed, publisher version kusw.oapolicy This item does not meet KU Open Access policy criteria. dc.rights.accessrights openAccess
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