TY - JOUR
T1 - Superapproximation Properties of the Interpolation Operator of Projection Type and Applications
AU - Zhang , Tie
AU - Lin , Yan-Ping
AU - Tait , R. J.
JO - Journal of Computational Mathematics
VL - 3
SP - 277
EP - 288
PY - 2002
DA - 2002/06
SN - 20
DO - http://doi.org/
UR - https://global-sci.org/intro/article_detail/jcm/8917.html
KW - Interpolation operator of projection type, Finite element, Superconvergence.
AB - <p style="text-align: justify;">Some superapproximation and ultra-approximation properties in function, gradient and two-order derivative approximations are shown for the interpolation operator of projection type on two-dimensional domain. Then, we consider the Ritz projection and Ritz-Volterra projection on finite element spaces, and by means of the superapproximation elementary estimates and Green function methods, derive the superconvergence and ultraconvergence error estimates for both projections, which are also the finite element approximation solutions of the elliptic problems and the Sobolev equations, respectively.</p>