TY - JOUR
T1 - Convergence Analysis of Finite Element Solution of One-Dimensional Singularly Perturbed Differential Equations on Equidistributing Meshes
AU - Huang , Weizhang
JO - International Journal of Numerical Analysis and Modeling
VL - 1
SP - 57
EP - 74
PY - 2005
DA - 2005/02
SN - 2
DO - http://doi.org/
UR - https://global-sci.org/intro/article_detail/ijnam/920.html
KW - mesh adaptation, equidistribution, error analysis, finite element method.
AB - <p style="text-align: justify;">In this paper convergence on equidistributing meshes is
investigated. Equidistributing meshes, or more generally approximate
equidistributing meshes, are constructed through the well-known
equidistribution principle and a so-called adaptation (or monitor)
function which is defined based on estimates on interpolation error for
polynomial preserving operators. Detailed convergence analysis is given
for finite element solution of singularly perturbed two-point boundary
value problems without turning points. Illustrative numerical results
are given for a convection-diffusion problem and a reaction-diffusion
problem.</p>