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.

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• L. Chen. Superconvergence of tetrahedral linear finite elements. International Journal of Numerical Analysis and Modeling, 3(3):273-282, 2006.

We estabilish superconvergence results on a class of 3-D meshes.

• L. Chen and H. Li. Superconvergence of Gradient Recovery Schemes on graded meshes for corner singularities. Journal of Computational Mathematics. 28, 11-31, 2010.

We show that superconvergence exists for a type of graded meshes for corner singularities in polygonal domains. In contrast to the existing superconvergence results, we do not assume high regularity of the exact solution.

• H. Wei, L. Chen and Y. Huang. Superconvergence and Gradient Recovery of Linear Finite Elements for the Laplace-Beltrami Operator on General Surfaces. Accepted by SIAM Journal on Numerical Analysis, 2010.

We establish superconvergence results and several gradient recovery methods of finite element methods to the surface linear finite element method on surfaces with mildly structured triangular meshes.