Browsing by Author "Wang, Xiaoshen"
Now showing 1 - 1 of 1
Results Per Page
Sort Options
Item Two-order superconvergence for a weak Galerkin method on rectangular and cuboid grids(Numerical Methods for Partial Differential Equations, 2022-09-22) Wang, Junping; Wang, Xiaoshen; Ye, Xiu; Zhang, Shangyou; Zhu, PengThis article introduces a particular weak Galerkin (WG) element on rectangular/cuboid partitions that uses k $$ k $$ th order polynomial for weak finite element functions and ( k + 1 ) $$ \left(k+1\right) $$ th order polynomials for weak derivatives. This WG element is highly accurate with convergence two orders higher than the optimal order in an energy norm and the L 2 $$ {L}^2 $$ norm. The superconvergence is verified analytically and numerically. Furthermore, the usual stabilizer in the standard weak Galerkin formulation is no longer needed for this element.