TY - JOUR
T1 - The Gradient Superconvergence of Bilinear Finite Volume Element for Elliptic Problems
AU - Tie Zhang &  Lixin Tang
JO - Numerical Mathematics: Theory, Methods and Applications
VL - 4
SP - 579
EP - 594
PY - 2016
DA - 2016/09
SN - 9
DO - http://doi.org/10.4208/nmtma.2016.m1515
UR - https://global-sci.org/intro/article_detail/nmtma/12390.html
KW - 
AB - <p style="text-align: justify;">We study the gradient superconvergence of bilinear finite volume
element (FVE) solving the elliptic problems. First, a superclose
weak estimate is established for the bilinear form of the FVE
method. Then, we prove that the gradient approximation of the FVE
solution has the superconvergence property: <br/></p><p style="text-align:center"><img src="http://admin.global-sci.org/uploads/ueditor/image/20201103/1604396426945408.png" title="1604396426945408.png" alt="image.png"/></p><p style="text-align: justify;">where <img src="http://admin.global-sci.org/uploads/ueditor/image/20201103/1604396720170466.png" title="1604396720170466.png" alt="image.png"/>&nbsp;denotes the average gradient on elements
containing point $P$ and $S$ is the set of optimal stress points
composed of the mesh points, the midpoints of edges and the centers of elements.<br/></p>