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Article

Lin, Runchang ; Zhang, Zhimin
Numerical study of natural superconvergence in least-squares finite element methods for elliptic problems. (English). Applications of Mathematics, vol. 54 (2009), issue 3, pp. 251-266
MSC: 35J05, 65N12, 65N30 | MR 2530542 | Zbl 1212.65419 | DOI: 10.1007/s10492-009-0016-6
Keywords:
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
Summary:
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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