Superconvergence

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

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


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