A superconvergent CDG finite element for the Poisson equation on polytopal meshes
Xiu Ye,
Shangyou Zhang
Abstract:A conforming discontinuous Galerkin (CDG) finite element is constructed for solving second order elliptic equations on polygonal and polyhedral meshes. The numerical trace on the edge between two elements is no longer the average of two discontinuous Pk functions on the two sides, but a lifted function from four Pk functions. When the numerical gradient space is the subspace of piecewise polynomials on subtriangles/subtehrahedra of a polygon/polyhedron T which have a one‐piece polynomial divergence on T, th… Show more
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