TY - JOUR
T1 - Low Regularity Error Analysis for Weak Galerkin Finite Element Methods for Second Order Elliptic Problems
AU - Ye , Xiu
AU - Zhang , Shangyou
JO - Numerical Mathematics: Theory, Methods and Applications
VL - 3
SP - 613
EP - 623
PY - 2021
DA - 2021/06
SN - 14
DO - http://doi.org/10.4208/nmtma.OA-2020-0120
UR - https://global-sci.org/intro/article_detail/nmtma/19191.html
KW - Weak Galerkin, finite element methods, weak gradient, second-order elliptic problems, low regularity.
AB - <p style="text-align: justify;">This paper presents error estimates in both an energy norm and the $L^2$-norm for the weak Galerkin (WG) finite element methods for elliptic problems with
low regularity solutions. The error analysis for the continuous Galerkin finite element remains same regardless of regularity. A totally different analysis is needed for
discontinuous finite element methods if the elliptic regularity is lower than H-1.5.
Numerical results confirm the theoretical analysis.</p>