Two‐order superconvergence for a weak Galerkin method on rectangular and cuboid grids.

This 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 L2$$ {L}^2 $$ 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. [ABSTRACT FROM AUTHOR]