TY - JOUR
T1 - A Modified Weak Galerkin Finite Element Method for Sobolev Equation
AU - Gao , Fuzheng
AU - Wang , Xiaoshen
JO - Journal of Computational Mathematics
VL - 3
SP - 307
EP - 322
PY - 2015
DA - 2015/06
SN - 33
DO - http://doi.org/10.4208/jcm.1502-m4509
UR - https://global-sci.org/intro/article_detail/jcm/9844.html
KW - Galerkin FEMs, Sobolev equation, Discrete weak gradient, Modified weak
Galerkin, Error estimate.
AB - <p style="text-align: justify;">For Sobolev equation, we present a new numerical scheme based on a modified weak Galerkin finite element method, in which differential operators are approximated by weak forms through the usual integration by parts. In particular, the numerical method allows the use of discontinuous finite element functions and arbitrary shape of element. Optimal order error estimates in discrete $H^1$ and $L^2$ norms are established for the corresponding modified weak Galerkin finite element solutions. Finally, some numerical results are given to verify theoretical results.</p>