Superconvergence

In numerical analysis, a superconvergent or supraconvergent method is one which converges faster than generally expected (superconvergence or supraconvergence). For example, in the Finite Element Method approximation to Poisson's equation in two dimensions, using piecewise linear elements, the average error in the gradient is first order. However under certain conditions it's possible to recover the gradient at certain locations within each element to second order.

References

• Barbeiro, S.; Ferreira, J. A.; Grigorieff, R. D. (2005), "Supraconvergence of a finite difference scheme for solutions in H^s(0, L)", IMA J Numer Anal 25 (4): 797–811, doi:10.1093/imanum/dri018 
• Ferreira, J. A.; Grigorieff, R. D. (1998), "On the supraconvergence of elliptic finite difference methods", Applied Numerical Mathematics 28: 275–292, doi:10.1016/S0168-9274(98)00048-8, https://estudogeral.sib.uc.pt/bitstream/10316/4663/1/filee39b5d5b0989429899f94ddf76537ee1.pdf 
• Levine, N. D. (1985), "Superconvergent Recovery of the Gradient from Piecewise Linear Finite-element Approximations", IMA J Numer Anal 5 (4): 407–427, doi:10.1093/imanum/5.4.407, http://www.nicklevine.org/sums/SuperconvergentRecoveryoftheGradientfromPiecewiseLinearFinite-elementApproximations.pdf