A $P_{k+2}$ polynomial lifting operator on polygons and polyhedrons
Numerical Analysis
2020-09-30 v1 Numerical Analysis
Abstract
A 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 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 and norms. The theory is confirmed by numerical solutions of 2D and 3D Poisson equations.
Cite
@article{arxiv.2009.13604,
title = {A $P_{k+2}$ polynomial lifting operator on polygons and polyhedrons},
author = {Xiu Ye and Shangyou Zhang},
journal= {arXiv preprint arXiv:2009.13604},
year = {2020}
}