@Article{IJNAM-5-152,
author = {M. Hamouda and H. V. J. Le Meur},
title = {Numerical Characterization of the Regularity Loss in Minimal Surfaces},
journal = {International Journal of Numerical Analysis and Modeling},
year = {2008},
volume = {5},
number = {1},
pages = {152--166},
abstract = {<p style="text-align: justify;">In this article, we numerically study the regularity loss of
the solutions of non-parametric minimal surfaces with non-zero boundary
conditions. Parts of the boundaries have non-positive mean curvature. As
expected from theoretical results in such geometry, we find that the
solutions may or may not satisfy the boundary conditions depending upon
the data. Firstly, we validate the numerical study on the astroid and
discuss the various kinds of non-regularity characterizations. We
provide an algorithm to test the regularity loss using the numerical
results. Secondly, we give a numerical estimate of the threshold value
of the boundary condition beyond which no regular solution exists. More
theoretical results are also given on the approximation by the
regularized solution of the non-regularized one. The regularized
solution exhibits a boundary layer. Finally, the study is applied to the
catenoid for which the exact threshold value is known. The exact value
and the computed one are in good agreement.</p>},
issn = {2617-8710},
doi = {https://doi.org/},
url = {http://global-sci.org/intro/article_detail/ijnam/804.html}
}