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least-squares finite element method; mixed finite element method; natural superconvergence; Raviart-Thomas element; Poisson equation; Lagrange elements; triangular and rectangular meshes; numerical experiments; Galerkin method
Natural superconvergence of the least-squares finite element method is surveyed for the one- and two-dimensional Poisson equation. For two-dimensional problems, both the families of Lagrange elements and Raviart-Thomas elements have been considered on uniform triangular and rectangular meshes. Numerical experiments reveal that many superconvergence properties of the standard Galerkin method are preserved by the least-squares finite element method.
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