TY - JOUR
T1 - Meshfree First-Order System Least Squares
AU - Hugh R. MacMillan, Max D. Gunzburger & John V. Burkardt
JO - Numerical Mathematics: Theory, Methods and Applications
VL - 1
SP - 29
EP - 43
PY - 2008
DA - 2008/01
SN - 1
DO - http://doi.org/
UR - https://global-sci.org/intro/article_detail/nmtma/6040.html
KW - Meshfree methods, first-order system least squares, adaptive finite elements.
AB - <p style="text-align: justify;">We prove convergence for a meshfree first-order system least squares (FOSLS)
partition of unity finite element method (PUFEM). Essentially, by virtue of the partition
of unity, local approximation gives rise to global approximation in $\mathrm{H}(div)\cap\mathrm{H}(curl)$.
The FOSLS formulation yields local a posteriori error estimates to guide the judicious
allotment of new degrees of freedom to enrich the initial point set in a meshfree discretization. Preliminary numerical results are provided and remaining challenges are
discussed.<br/></p>