TY - JOUR
T1 - Upwind Strategy for Localized Method of Approximate Particular Solutions with Applications to Convection Dominated Diffusion Problems
AU - Zhang , Xueying
AU - Ran , Luyu
JO - Advances in Applied Mathematics and Mechanics
VL - 2
SP - 455
EP - 466
PY - 2020
DA - 2020/12
SN - 13
DO - http://doi.org/10.4208/aamm.OA-2019-0103
UR - https://global-sci.org/intro/article_detail/aamm/18492.html
KW - LMAPS, convection dominated problems, upwind scheme, radial basis functions.
AB - <p style="text-align: justify;">A novel upwind technique for the localized method of approximate particular solutions (LMAPS) is proposed to solve the convection-diffusion equations. An upwind approximation to the convective terms is implemented by choosing upwind interpolation stencils while the central interpolation stencils are used for the diffusive terms. The proposed upwind LMAPS scheme is also been compared with conventional LMAPS without upwind technique, to demonstrate its superiority in generating high accurate solutions than the latter. Numerical results show that the proposed upwind LMAPS has high accuracy and efficiency for a variety of convection-diffusion equations.</p>