题目：An arbitrary-order discontinuous Galerkin method with one unknown per element
报告人: 明平兵 研究员（中国科学院数学与系统科学研究院）
We propose an arbitrary-order discontinuous Galerkin method for second-order elliptic problem on general polygonal mesh with only one degree of freedom per element. This is achieved by locally solving a discrete least-squares over a neighboring element patch. Under a geometrical condition on the element patch, we prove an optimal a priori error estimates in the energy norm and in the L$^2$ norm. The accuracy and the efficiency of the method up to order six on several polygonal meshes are illustrated by a set of benchmark problems that include elliptic equations of 2nd order and 4th order, in both two dimension and three dimension. This is a joint work with Rho Li, Ziyuan Sun and Zhijian Yang.