TY - JOUR
T1 - Error Estimation for Numerical Methods Using the Ultra Weak Variational Formulation in Model of Near Field Scattering Problem
AU - Tian Luan, Fuming Ma & Minghui Liu
JO - Journal of Computational Mathematics
VL - 5
SP - 491
EP - 506
PY - 2014
DA - 2014/10
SN - 32
DO - http://doi.org/10.4208/jcm.1403-m4404
UR - https://global-sci.org/intro/article_detail/jcm/9900.html
KW - Helmholtz equation, Ultra weak variational formulation, Plane wave function,
Evanescent wave function, Absorbing boundary condition.
AB - <p style="text-align: justify;">In this paper, we investigate the use of ultra weak variational formulation to solve a wave scattering problem in near field optics. In order to capture the sub-scale features of waves, we utilize evanescent wave functions together with plane wave functions to approximate the local properties of the field. We analyze the global convergence and give an error estimation of the method. Numerical examples are also presented to demonstrate the effectiveness of the strategy.</p>