TY - JOUR
T1 - A Comment on Least-Squares Finite Element Methods with Minimum Regularity Assumptions
JO - International Journal of Numerical Analysis and Modeling
VL - 4
SP - 899
EP - 903
PY - 2013
DA - 2013/10
SN - 10
DO - http://doi.org/
UR - https://global-sci.org/intro/article_detail/ijnam/602.html
KW - least-squares, finite element methods, Galerkin methods.
AB - <p style="text-align: justify;">Least-squares(LS) finite element methods are applied successfully to a wide range of problems arising from science and engineering. However, there are reservations to use LS methods
for problems with low regularity solutions. In this paper, we consider LS methods for second-order
elliptic problems using the minimum regularity assumption, i.e. the solution only belongs to $H^1$ space. We provide a theoretical analysis showing that LS methods are competitive alternatives
to mixed and standard Galerkin methods by establishing that LS solutions are bounded by the
mixed and standard Galerkin solutions.</p>