TY - JOUR
T1 - Multiscale Basis Functions for Singular Perturbation on Adaptively Graded Meshes
AU - Sun , Mei-Ling
AU - Jiang , Shan
JO - Advances in Applied Mathematics and Mechanics
VL - 5
SP - 604
EP - 614
PY - 2014
DA - 2014/06
SN - 6
DO - http://doi.org/10.4208/aamm.2013.m488
UR - https://global-sci.org/intro/article_detail/aamm/38.html
KW - Multiscale basis functions, singular perturbation, boundary layer, adaptively graded meshes.
AB - <p style="text-align: justify;">We apply the multiscale basis functions for the singularly perturbed
reaction-diffusion problem on adaptively graded meshes, which can provide a good
balance between the numerical accuracy and computational cost. The multiscale space
is built through standard finite element basis functions enriched with multiscale basis
functions. The multiscale basis functions have abilities to capture originally perturbed
information in the local problem, as a result, our method is capable of reducing the
boundary layer errors remarkably on graded meshes, where the layer-adapted meshes
are generated by a given parameter. Through numerical experiments we demonstrate
that the multiscale method can acquire second order convergence in the L<sup>2</sup> norm and
first order convergence in the energy norm on graded meshes, which is independent
of ε. In contrast with the conventional methods, our method is much more accurate
and effective.</p>