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# Superconvergence

In numerical analysis, a superconvergent method is one which converges faster than generally expected. 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

S. Barbeiro, J.A. Ferreira, R.D. Grigorieff, Supraconvergence of a finite difference scheme for solutions in H^s(0,L), IMA J Numer Anal. 2005; 25: 797-811

J.A. Ferreira, R.D. Grigorieff, On the supraconvergence elliptic finite difference methods, Applied Numerical Mathematics 1998; 28: 275-292

N.D. Levine, Superconvergent Recovery of the Gradient from Piecewise Linear Finite-element Approximations IMA J Numer Anal. 1985; 5: 407-427

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