TY - JOUR
T1 - Convergent Overdetermined-RBF-MLPG for Solving Second Order Elliptic PDEs
AU - Shirzadi , Ahmad
AU - Ling , Leevan
JO - Advances in Applied Mathematics and Mechanics
VL - 1
SP - 78
EP - 89
PY - 2013
DA - 2013/05
SN - 5
DO - http://doi.org/10.4208/aamm.11-m11168
UR - https://global-sci.org/intro/article_detail/aamm/58.html
KW - Local integral equations, meshless methods, radial basis functions, overdetermined
systems, solvability, convergence.
AB - <p style="text-align: justify;">This paper deals with the solvability and the convergence of a class of
unsymmetric Meshless Local Petrov-Galerkin (MLPG) method with radial
basis function (RBF) kernels generated trial spaces. Local weak-form
testings are done with step-functions. It is proved that
subject to sufficiently many appropriate testings, solvability of the
unsymmetric RBF-MLPG resultant systems can be guaranteed.
Moreover, an error analysis shows that this numerical approximation
converges at the same rate as found in RBF interpolation.
Numerical results (in double precision) give good agreement with
the provided theory.</p>