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Ultraconvergence of the patch recovery technique II. (English) Zbl 0936.65132
Summary: [For part I, see ibid. 85, No. 216, 1431-1437 (1996; Zbl 0853.65116).]
The ultraconvergence property of a gradient recovery technique proposed by O. C. Zienkiewicz and J. Z. Zhu [Int. J. Numer. Methods Eng. 33, No. 7, 1331-1364 (1992; Zbl 0769.73084)] is analyzed for the Laplace equation in the two-dimensional setting. Under the assumption that the pollution effect is not present or is properly controlled, it is shown that the convergence rate of the recovered gradient at an interior node is two orders higher than the optimal global convergence rate when even-order finite element spaces and local uniform rectangular meshes are used.

MSC:
65N30 Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs
65N12 Stability and convergence of numerical methods for boundary value problems involving PDEs
35J05 Laplace operator, Helmholtz equation (reduced wave equation), Poisson equation
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References:
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