TY - JOUR
T1 - Error Analysis of an Immersed Finite Element Method for Euler-Bernoulli Beam Interface Problems
JO - International Journal of Numerical Analysis and Modeling
VL - 6
SP - 822
EP - 841
PY - 2017
DA - 2017/10
SN - 14
DO - http://doi.org/
UR - https://global-sci.org/intro/article_detail/ijnam/10482.html
KW - Error estimation, interface problem, interface independent mesh, Euler-Bernoulli beam, Hermite cubic finite element, multi-point Taylor expansion, optimal convergence.
AB - <p style="text-align: justify;">This article presents an error analysis of a Hermite cubic immersed finite element (IFE)
method for solving interface problems of the differential equation modeling a Euler-Bernoulli beam
made up of multiple materials together with suitable jump conditions at material interfaces. The
analysis consists of three essential groups. The first group is about IFE functions including bounds
for the IFE shape functions and inverse inequalities. The second group is about error bounds for
IFE interpolation derived with a multi-point Taylor expansion technique. The last group, and
perhaps the most important group, is for proving the optimal convergence of the IFE solution
generated by the usual Galerkin scheme based on the Hermite cubic IFE space considered in this
article.</p>