TY - JOUR
T1 - Generalized Normal Derivatives and Their Applications in DDMs with Nonmatching Grids and DG Methods
AU - Qiya Hu
JO - Numerical Mathematics: Theory, Methods and Applications
VL - 4
SP - 383
EP - 409
PY - 2008
DA - 2008/01
SN - 1
DO - http://doi.org/
UR - https://global-sci.org/intro/article_detail/nmtma/6056.html
KW - Green's formula, generalized normal derivative, domain decomposition, nonmathing
grids, discontinuous Galerkin, error estimates.
AB - <p style="text-align: justify;">A class of normal-like derivatives for functions with low regularity defined
on Lipschitz domains are introduced and studied. It is shown that the new normal-like
derivatives, which are called the generalized normal derivatives, preserve the major properties of the existing standard normal derivatives. The generalized normal derivatives
are then applied to analyze the convergence of domain decomposition methods (DDMs)
with nonmatching grids and discontinuous Galerkin (DG) methods for second-order elliptic problems. The approximate solutions generated by these methods still possess
the optimal energy-norm error estimates, even if the exact solutions to the underlying
elliptic problems admit very low regularities.</p>