论文标题
$ p_ {k+2} $多边形和多边形的多项式起重操作员
A $P_{k+2}$ polynomial lifting operator on polygons and polyhedrons
论文作者
论文摘要
$ p_ {k+2} $多项式起重操作员在多边形和多面体上定义。它将不连续的多项式在多边形/多面体内部提升到一件式$ p_ {k+2} $多项式。使用此提升操作员，我们证明了较弱的Galerkin有限元解决方案，在此提升之后，以高于最佳订单的两个订单收敛，均以$ l^2 $和$ h^1 $ norms的规范收敛。该理论通过2D和3D泊松方程的数值解确认。
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.
