题目：An Arbitrary-Order Discontinuous Galerkin Method with One Unkown Per Element
Abstract：We discuss 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 for the energy norm and for the L2 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. The application of this method to plate bending problem will also be addressed. This is a joint work with Ruo Li, Ziyuan Sun and Zhijian Yang.
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