TY - JOUR
T1 - Least-Squares Finite Element Methods for First-Order Elliptic Systems
AU - Bochev , Pavel
JO - International Journal of Numerical Analysis and Modeling
VL - 1
SP - 49
EP - 64
PY - 2004
DA - 2004/01
SN - 1
DO - http://doi.org/
UR - https://global-sci.org/intro/article_detail/ijnam/965.html
KW - finite elements, least-squares, first-order elliptic systems.
AB - <p style="text-align: justify;">Least-squares principles use artificial &quot;energy&quot; functionals to provide
a Rayleigh-Ritz-like setting for the finite element method. These functionals
are defined in terms of PDE’s residuals and are not unique. We show that
viable methods result from reconciliation of a mathematical setting dictated by
the norm-equivalence of least-squares functionals with practicality constraints
dictated by the algorithmic design. We identify four universal patterns that
arise in this process and develop this paradigm for first-order ADN elliptic systems. Special attention is paid to the effects that each discretization pattern
has on the computational and analytic properties of finite element methods, including error estimates, conditioning of the algebraic systems and the existence
of efficient preconditioners.</p>