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Title: Superconvergence of High Order Finite Difference Schemes Based on Variational Formulation for Elliptic Equations
The classical continuous finite element method with Lagrangian Q^k basis reduces to a finite difference scheme when all the integrals are replaced by the (𝑘+1)×(𝑘+1) Gauss–Lobatto quadrature. We prove that this finite difference scheme is (𝑘+2)-th order accurate in the discrete 2-norm for an elliptic equation with Dirichlet boundary conditions, which is a superconvergence result of function values. We also give a convenient implementation for the case 𝑘=2, which is a simple fourth order accurate elliptic solver on a rectangular domain.  more » « less
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Journal of scientific computing
Medium: X
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National Science Foundation
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