TY - JOUR
T1 - A Modified Primal-Dual Weak Galerkin Finite Element Method for Second Order Elliptic Equations in Non-Divergence Form
AU - Wang , ​Chunmei
JO - International Journal of Numerical Analysis and Modeling
VL - 4
SP - 500
EP - 523
PY - 2021
DA - 2021/05
SN - 18
DO - http://doi.org/
UR - https://global-sci.org/intro/article_detail/ijnam/19112.html
KW - Primal-dual, weak Galerkin, finite element methods, non-divergence form, Cordès
condition, polyhedral meshes.
AB - <p style="text-align: justify;">A modified primal-dual weak Galerkin (M-PDWG) finite element method is designed
for the second order elliptic equation in non-divergence form. Compared with the existing PDWG
methods proposed in [6], the system of equations resulting from the M-PDWG scheme could be
equivalently simplified into one equation involving only the primal variable by eliminating the dual
variable (Lagrange multiplier). The resulting simplified system thus has significantly fewer degrees
of freedom than the one resulting from existing PDWG scheme. Optimal order error estimates
are derived for the numerical approximations in the discrete $H^2$-norm, $H^1$-norm and $L^2$-norm
respectively. Extensive numerical results are demonstrated for both the smooth and non-smooth
coefficients on convex and non-convex domains to verify the accuracy of the theory developed in
this paper.</p>