Lagrange Interpolation and Finite Element Superconvergence

  title={Lagrange Interpolation and Finite Element Superconvergence},
  author={Li Bo},
Abstract. We consider the finite element approximation of the Laplacian operator with the homogeneous Dirichlet boundary condition, and study the corresponding Lagrange interpolation in the context of finite element superconvergence. For ddimensional Qk-type elements with d ≥ 1 and k ≥ 1, we prove that the interpolation points must be the Lobatto points if the Lagrange interpolation and the finite element solution are superclose in H norm. For d-dimensional Pk-type elements, we consider the… CONTINUE READING
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