TY - JOUR
T1 - A Posteriori Error Estimation of Spectral and Spectral Element Methods for the Stokes/Darcy Coupled Problem
AU - Wang , Weiwei
AU - Xu , Chuanju
JO - Journal of Mathematical Study
VL - 1
SP - 85
EP - 110
PY - 2014
DA - 2014/03
SN - 47
DO - http://doi.org/10.4208/jms.v47n1.14.05
UR - https://global-sci.org/intro/article_detail/jms/10113.html
KW - A posteriori error, Stokes/Darcy coupled equations, Spectral method, Spectral element method.
AB - <p style="text-align: justify;">In this paper, we carry out an a posteriori error analysis of Legendre spectral
approximations to the Stokes/Darcy coupled equations. The spectral approximations
are based on a weak formulation of the coupled equations by using the Beavers-Joseph-Saffman interface condition. The main contribution of the paper consists of deriving
a number of posteriori error indicators and their upper and lower bounds for the single domain case. An extension of the upper bounds to the multi-domain case in the
spectral element framework is also given.</p>