A P_k+2 polynomial lifting operator on polygons and polyhedrons

09/28/2020
by   Xiu Ye, et al.
0

A P_k+2 polynomial lifting operator is defined on polygons and polyhedrons. It lifts discontinuous polynomials inside the polygon/polyhedron and on the faces to a one-piece P_k+2 polynomial. With this lifting operator, we prove that the weak Galerkin finite element solution, after this lifting, converges at two orders higher than the optimal order, in both L^2 and H^1 norms. The theory is confirmed by numerical solutions of 2D and 3D Poisson equations.

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