TY - JOUR
T1 - Superconvergence of the gradient approximation for weak Galerkin finite element methods on nonuniform rectangular partitions
AU - Li, Dan
AU - Wang, Chunmei
AU - Wang, Junping
N1 - Funding Information:
The research of Chunmei Wang was partially supported by National Science Foundation Award DMS-1849483.The research of Junping Wang was supported by the NSF IR/D program, while working at National Science Foundation. However, any opinion, finding, and conclusions or recommendations expressed in this material are those of the author and do not necessarily reflect the views of the National Science Foundation.
Publisher Copyright:
© 2019 IMACS
PY - 2020/4
Y1 - 2020/4
N2 - This article presents a superconvergence for the gradient approximation of the second order elliptic equation discretized by weak Galerkin finite element methods on nonuniform rectangular partitions. The result shows a convergence of O(hr), 1.5≤r≤2, for the numerical gradient obtained from the lowest order weak Galerkin element consisting of piecewise linear and constant functions. For this numerical scheme, the optimal order of error estimate is O(h) for the gradient approximation. The superconvergence reveals a superior performance of the weak Galerkin finite element methods. Some computational results are included to numerically validate the superconvergence theory.
AB - This article presents a superconvergence for the gradient approximation of the second order elliptic equation discretized by weak Galerkin finite element methods on nonuniform rectangular partitions. The result shows a convergence of O(hr), 1.5≤r≤2, for the numerical gradient obtained from the lowest order weak Galerkin element consisting of piecewise linear and constant functions. For this numerical scheme, the optimal order of error estimate is O(h) for the gradient approximation. The superconvergence reveals a superior performance of the weak Galerkin finite element methods. Some computational results are included to numerically validate the superconvergence theory.
KW - Finite element methods
KW - Nonuniform rectangular partitions
KW - Second order elliptic equations
KW - Superconvergence
KW - Weak Galerkin
UR - http://www.scopus.com/inward/record.url?scp=85074508311&partnerID=8YFLogxK
U2 - 10.1016/j.apnum.2019.10.013
DO - 10.1016/j.apnum.2019.10.013
M3 - Article
AN - SCOPUS:85074508311
VL - 150
SP - 396
EP - 417
JO - Applied Numerical Mathematics
JF - Applied Numerical Mathematics
SN - 0168-9274
ER -